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Jacobiâs cubic analog of the pentagonal number theorem and representations of $$24n+5$$ as a sum of two squares
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2025
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Cristina Ballantine
Mircea Merca
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Partitions and elementary symmetric polynomials: an experimental approach
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2025
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Cristina Ballantine
George R. Beck
Mircea Merca
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Linear Dependencies Among Cubic Partition Numbers
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2025
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Cristina Ballantine
Mircea Merca
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PDF
Chat
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Do perfect powers repel partition numbers?
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2025
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Mircea Merca
Ken Ono
WeiâLun Tsai
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Elementary Symmetric Partitions
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2024
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Cristina Ballantine
George R. Beck
Mircea Merca
Bruce E. Sagan
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PDF
Chat
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Elementary symmetric partitions
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2024
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Cristina Ballantine
George R. Beck
Mircea Merca
Bruce E. Sagan
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+
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Overpartitions in terms of 2-adic valuation
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2024
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Mircea Merca
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+
PDF
Chat
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Partitions and elementary symmetric polynomials -- an experimental
approach
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2024
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Cristina Ballantine
George R. Beck
Mircea Merca
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On the sum of parts with multiplicity at least 2 in all the partitions of <i>n</i>
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2024
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Mircea Merca
Ae Ja Yee
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+
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Eulerâs partition function in terms of 2-adic valuation
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2024
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Mircea Merca
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PDF
Chat
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From sums of divisors to partition congruences
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2024
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Mircea Merca
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+
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Durfee Rectangle Identities via Symmetric Functions
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2024
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Cristina Ballantine
Mircea Merca
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+
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The Euler-Riemann Zeta Function with Even Arguments in Terms of Binomial Coefficients
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2023
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Mircea Merca
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PDF
Chat
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Plane Partitions and Divisors
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2023
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Cristina Ballantine
Mircea Merca
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PDF
Chat
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Plane Partitions and a Problem of Josephus
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2023
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Mircea Merca
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A further look at the sum of the parts with the same parity in the partitions of n
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2023
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George E. Andrews
Mircea Merca
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PDF
Chat
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n-Color Partitions into Distinct Parts as Sums over Partitions
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2023
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Mircea Merca
Emil Simion
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PDF
Chat
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Congruences modulo <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mn>4</mml:mn></mml:math> for the number of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mn>3</mml:mn></mml:math>-regular partitions
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2023
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Cristina Ballantine
Mircea Merca
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PDF
Chat
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Plane Partitions as Sums over Partitions
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2023
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Mircea Merca
I Radu
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+
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Additive evaluations of the number of divisors
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2023
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Mircea Merca
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+
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6-regular partitions: new combinatorial properties, congruences, and linear inequalities
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2023
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Cristina Ballantine
Mircea Merca
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+
PDF
Chat
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A q-Series Congruence Inspired by Andrews and Ramanujan
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2023
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Mircea Merca
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+
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Linear inequalities concerning the sum of the distinct parts congruent to <i>r</i> modulo <i>m</i> in all the partitions of <i>n</i>
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2023
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Mircea Merca
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+
PDF
Chat
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4-regular partitions and the pod function
|
2023
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Cristina Ballantine
Mircea Merca
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+
PDF
Chat
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From Symmetric Functions to Partition Identities
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2023
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Mircea Merca
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+
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$6$-regular partitions: new combinatorial properties, congruences, and linear inequalities
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2023
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Cristina Ballantine
Mircea Merca
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+
PDF
Chat
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Dysonâs crank and unimodal compositions
|
2022
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Cristina Ballantine
Mircea Merca
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+
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A reversal of Schurâs partition theorem
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2022
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Mircea Merca
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PDF
Chat
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New Combinatorial Interpretations for the Partitions into Odd Parts Greater than One
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2022
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Cristina Ballantine
Mircea Merca
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+
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Ramanujan-type congruences modulo 4 for partitions into distinct parts
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2022
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Mircea Merca
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PDF
Chat
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Families of Ramanujan-Type Congruences Modulo 4 for the Number of Divisors
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2022
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Mircea Merca
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PDF
Chat
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On Ramanujan-type congruences for multiplicative functions
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2022
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William Craig
Mircea Merca
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+
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Generalizations of Stanleyâs Theorem: Combinatorial Proofs and Related Inequalities
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2022
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Cristina Ballantine
Mircea Merca
|
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+
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Dyson's crank and unimodal compositions
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2022
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Cristina Ballantine
Mircea Merca
|
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+
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Parity of 3-regular partition numbers and Diophantine equations
|
2022
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Cristina Ballantine
Mircea Merca
Cristian-Silviu Radu
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PDF
Chat
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On Ramanujan-type Congruences for Multiplicative Functions
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2021
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William Craig
Mircea Merca
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+
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Connections Between Partitions and Divisors Related to the Parity of the Partition Function
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2021
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Mircea Merca
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PDF
Chat
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Distinct partitions and overpartitions
|
2021
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Mircea Merca
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+
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A further look at cubic partitions
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2021
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Mircea Merca
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+
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Alignments of permutations: their number, mean number, and total number of cycles
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2021
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Cristina Ballantine
Mircea Merca
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+
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A further look at a generalization of Waringâs formula
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2021
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Mircea Merca
|
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+
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On the Ramanujan-type congruences modulo 8 for the overpartitions into odd parts
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2021
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Mircea Merca
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+
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Almost 3-regular overpartitions
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2021
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Cristina Ballantine
Mircea Merca
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+
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Rank partition functions and truncated theta identities
|
2021
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Mircea Merca
|
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+
PDF
Chat
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On a nonlinear relation for computing the overpartition function
|
2021
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Mircea Merca
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+
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Linear inequalities concerning partitions into distinct parts
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2021
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Mircea Merca
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+
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Combinatorial interpretations of two identities of Guo and Yang
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2021
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Mircea Merca
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+
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Fubini polynomials and integer partitions
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2021
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Mircea Merca
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+
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Geometric polynomials and integer partitions
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2021
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Mircea Merca
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+
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Combinatorial interpretations of two identities of Guo and Yang
|
2021
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Mircea Merca
|
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+
PDF
Chat
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Combinatorial proof of the minimal excludant theorem
|
2021
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Cristina Ballantine
Mircea Merca
|
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+
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Connections between Fibonacci and Pell numbers
|
2021
|
Mircea Merca
|
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+
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On the number of partitions into parts not congruent to 0, $$\pm 3 \pmod {12}$$
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2021
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Mircea Merca
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+
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Generalized Lambert Series and Eulerâs Pentagonal Number Theorem
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2021
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Mircea Merca
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+
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Overpartitions and functions from multiplicative number theory
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2021
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Mircea Merca
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+
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A Theta Identity of Gauss Connecting Functions from Additive and Multiplicative Number Theory
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2021
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Mircea Merca
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+
PDF
Chat
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Infinite Product Formulae for Generating Functions for Sequences of Squares
|
2021
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Christian Krattenthaler
Mircea Merca
Cristian-Silviu Radu
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+
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On Ramanujan-type Congruences for Multiplicative Functions
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2021
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William Craig
Mircea Merca
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+
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$4$-Regular partitions and the pod function
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2021
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Cristina Ballantine
Mircea Merca
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+
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ON THE SUM OF PARTS IN THE PARTITIONS OF <i>n</i> INTO DISTINCT PARTS
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2020
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Mircea Merca
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+
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The reciprocal of $$(q;q)_n$$ as sums over partitions
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2020
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Mircea Merca
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+
PDF
Chat
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The powers of two as sums over partitions
|
2020
|
Mircea Merca
|
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+
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On a nonlinear relation for computing the overpartition function.
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2020
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Mircea Merca
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+
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The powers of two as sums over partitions
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2020
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Mircea Merca
|
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+
PDF
Chat
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On the sum of parts with multiplicity at least 2 in all the partitions of n
|
2020
|
Mircea Merca
Ae Ja Yee
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+
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Polygonal numbers and RogersâRamanujanâGordon theorem
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2020
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Mircea Merca
|
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+
PDF
Chat
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q-Series congruences involving statistical mechanics partition functions in regime III and IV of Baxterâs solution of the hard-hexagon model
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2020
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Mircea Merca
|
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+
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Rank partition functions and truncated theta identities
|
2020
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Mircea Merca
|
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+
PDF
Chat
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On the partitions into distinct parts and odd parts
|
2020
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Mircea Merca
|
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+
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$q$-Series congruences involving statistical mechanics partition functions in regime III and IV of Baxter's solution of the hard-hexagon model
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2020
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Mircea Merca
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+
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The r-Stirling numbers of the first kind in terms of the MĂśbius function
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2020
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Cristina Ballantine
Mircea Merca
|
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+
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On the partitions into distinct parts and odd parts.
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2020
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Mircea Merca
|
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+
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A generalization of complete and elementary symmetric functions
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2020
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Moussa Ahmia
Mircea Merca
|
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+
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On the Number of Even Parts in All Partitions of $$\varvec{n}$$ into Distinct Parts
|
2020
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George E. Andrews
Mircea Merca
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+
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Combinatorial interpretations of two identities of Guo and Yang
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2020
|
Mircea Merca
|
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+
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Truncated theta series and partitions into distinct parts
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2020
|
Mircea Merca
|
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+
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On a nonlinear relation for computing the overpartition function
|
2020
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Mircea Merca
|
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+
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The powers of two as sums over partitions
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2020
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Mircea Merca
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+
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Rank partition functions and truncated theta identities
|
2020
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Mircea Merca
|
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+
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$q$-Series congruences involving statistical mechanics partition functions in regime III and IV of Baxter's solution of the hard-hexagon model
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2020
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Mircea Merca
|
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+
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On the partitions into distinct parts and odd parts
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2020
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Mircea Merca
|
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+
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A generalization of complete and elementary symmetric functions
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2020
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Moussa Ahmia
Mircea Merca
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+
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ON THE NUMBER OF PARTITIONS INTO PARTS WITH THE MINIMAL PART k AND THE MINIMAL DIFFERENCE d
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2020
|
Mircea Merca
|
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+
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Infinite product formulae for generating functions for sequences of squares
|
2019
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Christian Krattenthaler
Mircea Merca
Cristian-Silviu Radu
|
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+
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Bernoulli numbers and symmetric functions
|
2019
|
Mircea Merca
|
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+
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Combinatorial proofs of two theorems related to the number of even parts in all partitions of n into distinct parts
|
2019
|
Cristina Ballantine
Mircea Merca
|
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+
PDF
Chat
|
On identities of Watson type
|
2019
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Cristina Ballantine
Mircea Merca
|
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+
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A Truncated Theta Identity of Gauss and Overpartitions into Odd Parts
|
2019
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Mircea Merca
Chun Wang
Ae Ja Yee
|
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+
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A Truncated Theta Identity of Gauss and Overpartitions into Odd Parts
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2019
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Mircea Merca
Chun Wang
Ae Ja Yee
|
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+
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On Two Truncated Quintuple Series Theorems
|
2019
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Mircea Merca
|
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+
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Combinatorial Proof of the Minimal Excludant Theorem
|
2019
|
Cristina Ballantine
Mircea Merca
|
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+
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A general method for proving the non-trivial linear homogeneous partition inequalities
|
2019
|
Mircea Merca
Jacob Katriel
|
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+
PDF
Chat
|
Bisected theta series, least r-gaps in partitions, and polygonal numbers
|
2019
|
Cristina Ballantine
Mircea Merca
|
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+
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Two Symmetric Identities Involving Complete and Elementary Symmetric Functions
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2019
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Mircea Merca
|
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+
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On lacunary recurrences with gaps of length four and eight for the Bernoulli numbers
|
2019
|
Mircea Merca
|
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+
PDF
Chat
|
Factorization theorems for generalized Lambert series and applications
|
2019
|
Mircea Merca
Maxie D. Schmidt
|
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+
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Jacobiâs Four and Eight Squares Theorems and Partitions into Distinct Parts
|
2019
|
Cristina Ballantine
Mircea Merca
|
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+
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Truncated Theta Series and Rogers-Ramanujan Functions
|
2019
|
Mircea Merca
|
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+
PDF
Chat
|
A family of lacunary recurrences for Fibonacci numbers
|
2019
|
Cristina Ballantine
Mircea Merca
|
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+
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Infinite product formulae for generating functions for sequences of squares
|
2019
|
Christian Krattenthaler
Mircea Merca
Cristian-Silviu Radu
|
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+
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Combinatorial Proof of the Minimal Excludant Theorem
|
2019
|
Cristina Ballantine
Mircea Merca
|
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+
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Some notes on the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" id="d1e22" altimg="si6.gif"><mml:mrow><mml:mo>(</mml:mo><mml:mi>q</mml:mi><mml:mo>,</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>-Stirling numbers
|
2018
|
Mircea Merca
|
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+
PDF
Chat
|
A Partition Identity Related to Stanleyâs Theorem
|
2018
|
Mircea Merca
Maxie D. Schmidt
|
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+
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Combinatorial proofs of two truncated theta series theorems
|
2018
|
Cristina Ballantine
Mircea Merca
Donny Passary
Ae Ja Yee
|
|
+
PDF
Chat
|
EulerâRiemann Zeta Function and ChebyshevâStirling Numbers of the First Kind
|
2018
|
Cristina Ballantine
Mircea Merca
|
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+
PDF
Chat
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The partition function p(n) in terms of the classical MĂśbius function
|
2018
|
Mircea Merca
Maxie D. Schmidt
|
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+
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New Connections Between Functions from Additive and Multiplicative Number Theory
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2018
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Mircea Merca
|
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+
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On the number of partitions into odd parts or congruent to $\pm 2 \pmod{10}$
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2018
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Mircea Merca
|
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+
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A $q$-analogue for sums of powers
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2018
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Mircea Merca
|
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+
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Factorization Theorems for Generalized Lambert Series and Applications
|
2017
|
Mircea Merca
Maxie D. Schmidt
|
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+
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Generalizations of two identities of Guo and Yang
|
2017
|
Mircea Merca
|
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+
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Truncated theta series and a problem of Guo and Zeng
|
2017
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George E. Andrews
Mircea Merca
|
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+
PDF
Chat
|
An infinite sequence of inequalities involving special values of the Riemann zeta function
|
2017
|
Mircea Merca
|
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+
PDF
Chat
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An infinite sequence of inequalities involving special values of the Riemann zeta function
|
2017
|
Mircea Merca
|
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+
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Bisected theta series, least $r$-gaps in partitions, and polygonal numbers
|
2017
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Cristina Ballantine
Mircea Merca
|
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+
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Binomial transforms and integer partitions into parts of k different magnitudes
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2017
|
Mircea Merca
|
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+
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Lambert series and conjugacy classes in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="mml1" display="inline" overflow="scroll" altimg="si1.gif"><mml:mi>G</mml:mi><mml:mi>L</mml:mi></mml:math>
|
2017
|
Mircea Merca
|
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+
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The Riemann Zeta Function With Even Arguments as Sums Over Integer Partitions
|
2017
|
Mircea Merca
|
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+
PDF
Chat
|
Inequalities involving the generating function for the number of partitions into odd parts
|
2017
|
Cristina Ballantine
Mircea Merca
|
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+
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On the Arithmetic Mean of the Square Roots of the First <i>n</i> Positive Integers
|
2017
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Mircea Merca
|
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+
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New relations for the number of partitions with distinct even parts
|
2017
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Mircea Merca
|
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+
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The Lambert series factorization theorem
|
2017
|
Mircea Merca
|
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+
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On the number of partitions into parts of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="mml1" display="inline" overflow="scroll" altimg="si1.gif"><mml:mi>k</mml:mi></mml:math> different magnitudes
|
2017
|
Mircea Merca
|
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+
PDF
Chat
|
On the Song recurrence relation for the Riemann zeta function
|
2017
|
Mircea Merca
|
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+
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New Factor Pairs for Factorizations of Lambert Series Generating Functions
|
2017
|
Mircea Merca
Maxie D. Schmidt
|
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+
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New recurrences for Euler''s partition function
|
2017
|
Mircea Merca
|
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+
PDF
Chat
|
Finite differences of Euler's zeta function
|
2017
|
Cristina Ballantine
Mircea Merca
|
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+
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Bisected theta series, least $r$-gaps in partitions, and polygonal numbers
|
2017
|
Cristina Ballantine
Mircea Merca
|
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+
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Factorization Theorems for Generalized Lambert Series and Applications
|
2017
|
Mircea Merca
Maxie D. Schmidt
|
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+
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Generating Special Arithmetic Functions by Lambert Series Factorizations
|
2017
|
Mircea Merca
Maxie D. Schmidt
|
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+
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From a Rogersâs identity to overpartitions
|
2016
|
Mircea Merca
|
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+
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Parity of sums of partition numbers and squares in arithmetic progressions
|
2016
|
Cristina Ballantine
Mircea Merca
|
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+
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New convolutions for complete and elementary symmetric functions
|
2016
|
Mircea Merca
|
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+
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New convolutions for the number of divisors
|
2016
|
Cristina Ballantine
Mircea Merca
|
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+
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On families of linear recurrence relations for the special values of the Riemann zeta function
|
2016
|
Mircea Merca
|
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+
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Connections between central factorial numbers and Bernoulli polynomials
|
2016
|
Mircea Merca
|
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+
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Fast computation of the partition function
|
2016
|
Mircea Merca
|
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+
PDF
Chat
|
Padovan numbers as sums over partitions into odd parts
|
2016
|
Cristina Ballantine
Mircea Merca
|
|
+
PDF
Chat
|
A new look on the truncated pentagonal number theorem
|
2016
|
Mircea Merca
|
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+
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Stirling numbers and integer partitions
|
2015
|
Mircea Merca
|
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+
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A note on the partitions involving parts of k different magnitudes
|
2015
|
Mircea Merca
|
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+
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Asymptotics of the ChebyshevâStirling numbers of the first kind
|
2015
|
Mircea Merca
|
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+
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The cardinal sine function and the ChebyshevâStirling numbers
|
2015
|
Mircea Merca
|
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+
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Combinatorial interpretations of a recent convolution for the number of divisors of a positive integer
|
2015
|
Mircea Merca
|
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+
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The bisectional pentagonal number theorem
|
2015
|
Mircea Merca
|
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+
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A connection between JacobiâStirling numbers and Bernoulli polynomials
|
2015
|
Mircea Merca
|
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+
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An Alternative to Faulhaber's Formula
|
2015
|
Mircea Merca
|
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+
PDF
Chat
|
A double inequality involving ErdĹs-Borwein constants
|
2015
|
Mircea Merca
|
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+
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A new look on the generating function for the number of divisors
|
2014
|
Mircea Merca
|
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+
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Some experiments with complete and elementary symmetric functions
|
2014
|
Mircea Merca
|
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+
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Inequalities involving the generating function for the number of partitions into odd parts
|
2014
|
Cristina Ballantine
Mircea Merca
|
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+
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A new connection between<i>r</i>-Whitney numbers and Bernoulli polynomials
|
2014
|
Mircea Merca
|
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+
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A generalization of Eulerâs pentagonal number recurrence for the partition function
|
2014
|
Mircea Merca
|
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+
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New upper bounds for the number of partitions into a given number of parts
|
2014
|
Mircea Merca
|
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+
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A generalization of the symmetry between complete and elementary symmetric functions
|
2014
|
Mircea Merca
|
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+
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On Some Power Sums of Sine or Cosine
|
2014
|
Mircea Merca
|
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+
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Inequalities involving the generating function for the number of partitions into odd parts
|
2014
|
Cristina Ballantine
Mircea Merca
|
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+
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A Note on q-Stirling Numbers
|
2014
|
Mircea Merca
|
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+
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A note on the JacobiâStirling numbers
|
2013
|
Mircea Merca
|
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+
PDF
Chat
|
A note on the r-Whitney numbers of Dowling lattices
|
2013
|
Mircea Merca
|
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+
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An asymptotic formula of cosine power sums
|
2013
|
Mircea Merca
Tanfer TanrÄąverdi
|
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+
PDF
Chat
|
A note on the determinant of a Toeplitz-Hessenberg matrix
|
2013
|
Mircea Merca
|
|
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A convolution for complete and elementary symmetric functions
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2012
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Mircea Merca
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The truncated pentagonal number theorem
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2012
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George E. Andrews
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A Special Case of the Generalized Girard-Waring Formula
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2012
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Mircea Merca
Alejandro Cuza
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A Note on Cosine Power Sums
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2012
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Mircea Merca
Alejandro Cuza
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Fast Algorithm for Generating Ascending Compositions
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2011
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Mircea Merca
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Inequalities and Identities Involving Sums of Integer Functions
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2011
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Mircea Merca
Constantin Istrati
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