|
+
|
GAUSSIAN INEQUALITY
|
2024
|
Tewodros Amdeberhan
David Callan
|
|
+
PDF
Chat
|
Inversion Sequences Avoiding Quadruple Length-3 Patterns
|
2023
|
David Callan
Toufik Mansour
|
|
+
PDF
Chat
|
The number of {1243, 2134}-avoiding permutations
|
2023
|
David Callan
|
|
+
|
Restricted inversion sequences and Schröder paths
|
2023
|
David Callan
Toufik Mansour
|
|
+
|
Gaussian inequality
|
2023
|
Tewodros Amdeberhan
David Callan
|
|
+
PDF
Chat
|
Permutations avoiding 4321 and 3241 have an algebraic generating function
|
2022
|
David Callan
|
|
+
|
An involution on set partitions
|
2022
|
David Callan
|
|
+
|
A bijection for Delannoy paths
|
2022
|
David Callan
|
|
+
|
A Note on Generalized Narayana Numbers
|
2022
|
David Callan
|
|
+
|
A Combinatorial Interpretation for Sequence A345973 in OEIS
|
2021
|
David Callan
|
|
+
|
Some bijections for lattice paths
|
2021
|
David Callan
|
|
+
|
A Combinatorial Interpretation for Sequence A345973 in OEIS
|
2021
|
David Callan
|
|
+
|
On Ascent, Repetition and Descent Sequences
|
2019
|
David Callan
|
|
+
|
Enumeration of permutations avoiding a triple of 4-letter patterns is almost all done
|
2019
|
David Callan
Toufik Mansour
Mark Shattuck
|
|
+
|
On Ascent, Repetition and Descent Sequences
|
2019
|
David Callan
|
|
+
PDF
Chat
|
Enumeration of small Wilf classes avoiding 1342 and two other 4-letter patterns
|
2018
|
David Callan
Toufik Mansour
|
|
+
PDF
Chat
|
Enumeration of small Wilf classes avoiding 1324 and two other 4-letter patterns
|
2018
|
David Callan
Toufik Mansour
|
|
+
|
Enumeration of 2-Wilf Classes of Four 4-letter Patterns
|
2017
|
David Callan
Toufik Mansour
|
|
+
|
Enumeration of small Wilf classes avoiding 1342 and two other $4$-letter patterns
|
2017
|
David Callan
Toufik Mansour
|
|
+
PDF
Chat
|
On permutations avoiding 1324, 2143, and another 4-letter pattern
|
2017
|
David Callan
Toufik Mansour
|
|
+
PDF
Chat
|
On permutations avoiding 1243, 2134, and another 4-letter pattern
|
2017
|
David Callan
Toufik Mansour
|
|
+
|
Enumeration small classes of 1324 and other two $4$-letter patterns
|
2017
|
David Callan
Toufik Mansour
|
|
+
|
Enumeration of small Wilf classes avoiding 1324 and two other 4-letter patterns
|
2017
|
David Callan
Toufik Mansour
|
|
+
|
Wilf classification of triples of 4-letter patterns I
|
2017
|
David Callan
Toufik Mansour
Mark Shattuck
|
|
+
|
Bijections for Dyck paths with all peak heights of the same parity
|
2017
|
David Callan
|
|
+
|
Enumeration of permutations avoiding a triple of 4-letter patterns is all done
|
2017
|
David Callan
Toufik Mansour
Mark Shattuck
|
|
+
|
Revitalized Automatic Proofs: Demonstrations.
|
2017
|
Tewodros Amdeberhan
David Callan
Hideyuki Ohtsuka
Roberto Tauraso
|
|
+
|
Enumeration of small Wilf classes avoiding 1342 and two other $4$-letter patterns
|
2017
|
David Callan
Toufik Mansour
|
|
+
|
Bijections for Dyck paths with all peak heights of the same parity
|
2017
|
David Callan
|
|
+
|
Enumeration of small Wilf classes avoiding 1324 and two other 4-letter patterns
|
2017
|
David Callan
Toufik Mansour
|
|
+
|
Restricted Stirling Permutations
|
2016
|
David Callan
Shi-Mei Ma
Toufik Mansour
|
|
+
|
Restricted Stirling permutations
|
2016
|
David Callan
Shi-Mei Ma
Toufik Mansour
|
|
+
|
A bijection for two sequences in OEIS
|
2016
|
David Callan
|
|
+
|
A note on a bijection for Schröder permutations
|
2016
|
David Callan
|
|
+
|
Five subsets of permutations enumerated as weak sorting permutations
|
2016
|
David Callan
Toufik Mansour
|
|
+
|
Wilf classification of triples of 4-letter patterns
|
2016
|
David Callan
Toufik Mansour
Mark Shattuck
|
|
+
|
Revitalized automatic proofs: demonstrations
|
2016
|
Tewodros Amdeberhan
David Callan
Hideyuki Ohtsuka
Roberto Tauraso
|
|
+
|
Restricted Stirling permutations
|
2016
|
David Callan
Shi-Mei Ma
Toufik Mansour
|
|
+
|
A bijection for two sequences in OEIS
|
2016
|
David Callan
|
|
+
PDF
Chat
|
Some identities for derangement and Ward number sequences and related bijections
|
2015
|
David Callan
Toufik Mansour
Mark Shattuck
|
|
+
PDF
Chat
|
Some Combinatorial Arrays Related to the Lotka-Volterra System
|
2015
|
David Callan
Shi-Mei Ma
Toufik Mansour
|
|
+
|
A sign-reversing involution to count labeled lone-child-avoiding trees
|
2014
|
David Callan
|
|
+
|
On permutations avoiding the dashed patterns 32-41 and 41-32
|
2014
|
David Callan
|
|
+
|
Restricted ascent sequences and Catalan numbers
|
2014
|
David Callan
Toufik Mansour
Mark Shattuck
|
|
+
|
Another bijection for 021-avoiding ascent sequences
|
2014
|
David Callan
|
|
+
|
Some combinatorial arrays related to the Lotka-Volterra system
|
2014
|
Shi-Mei Ma
Toufik Mansour
David Callan
|
|
+
PDF
Chat
|
Restricted ascent sequences and Catalan numbers
|
2014
|
David Callan
Toufik Mansour
Mark Shattuck
|
|
+
|
A sign-reversing involution to count labeled lone-child-avoiding trees
|
2014
|
David Callan
|
|
+
|
Restricted ascent sequences and Catalan numbers
|
2014
|
David Callan
Toufik Mansour
Mark Shattuck
|
|
+
|
On permutations avoiding the dashed patterns 32-41 and 41-32
|
2014
|
David Callan
|
|
+
|
Permutations avoiding 4321 and 3241 have an algebraic generating function
|
2013
|
David Callan
|
|
+
|
The number of {1243, 2134}-avoiding permutations
|
2013
|
David Callan
|
|
+
|
An application of a bijection of Mansour, Deng, and Du
|
2012
|
David Callan
|
|
+
|
The run transform
|
2012
|
David Callan
Emeric Deutsch
|
|
+
|
An identity for the central binomial coefficient
|
2012
|
David Callan
|
|
+
|
Kreweras's Narayana number identity has a simple Dyck path interpretation
|
2012
|
David Callan
|
|
+
|
A variant of Touchard's Catalan number identity
|
2012
|
David Callan
|
|
+
|
Flexagons Lead to a Catalan Number Identity
|
2012
|
David Callan
|
|
+
|
An application of a bijection of Mansour, Deng, and Du
|
2012
|
David Callan
|
|
+
|
The Run Transform
|
2011
|
David Callan
Emeric Deutsch
|
|
+
|
A permutation pattern that illustrates the strong law of small numbers
|
2011
|
David Callan
|
|
+
|
The number of bar{3}bar{1}542-avoiding permutations
|
2011
|
David Callan
|
|
+
|
A combinatorial interpretation of the Catalan transform of the Catalan numbers
|
2011
|
David Callan
|
|
+
|
The number of \bar{2}413\bar{5}-avoiding permutations
|
2011
|
David Callan
|
|
+
|
The number of bar{3}bar{1}542-avoiding permutations
|
2011
|
David Callan
|
|
+
|
A combinatorial interpretation of the Catalan transform of the Catalan numbers
|
2011
|
David Callan
|
|
+
|
A permutation pattern that illustrates the strong law of small numbers
|
2011
|
David Callan
|
|
+
|
The Run Transform
|
2011
|
David Callan
Emeric Deutsch
|
|
+
|
Lagrange Inversion Counts $3\bar{5}241$-Avoiding Permutations
|
2011
|
David Callan
|
|
+
|
A bijection to count (1-23-4)-avoiding permutations
|
2010
|
David Callan
|
|
+
|
Flexagons yield a curious Catalan number identity
|
2010
|
David Callan
|
|
+
|
A bijection to count (1-23-4)-avoiding permutations
|
2010
|
David Callan
|
|
+
|
Klazar trees and perfect matchings
|
2009
|
David Callan
|
|
+
|
A combinatorial survey of identities for the double factorial
|
2009
|
David Callan
|
|
+
PDF
Chat
|
Pattern avoidance in “flattened” partitions
|
2008
|
David Callan
|
|
+
PDF
Chat
|
Circular Digraph Walks, $k$-Balanced Strings, Lattice Paths and Chebychev Polynomials
|
2008
|
Evangelos Georgiadis
David Callan
Qing-Hu Hou
|
|
+
|
A Combinatorial Interpretation for an Identity of Barrucand
|
2008
|
David Callan
|
|
+
|
Card deals, lattice paths, abelian words and combinatorial identities
|
2008
|
David Callan
|
|
+
|
Pattern avoidance in "flattened" partitions
|
2008
|
David Callan
|
|
+
|
Circular Digraph Walks, k-Balanced Strings, Lattice Paths and Chebychev Polynomials
|
2008
|
Evangelos Georgiadis
David Callan
Qing-Hu Hou
|
|
+
|
Klazar trees and perfect matchings
|
2008
|
David Callan
|
|
+
|
Sets, Lists and Noncrossing Partitions
|
2007
|
David Callan
|
|
+
|
On Generating Functions Involving the Square Root of a Quadratic Polynomial
|
2007
|
David Callan
|
|
+
PDF
Chat
|
A Bijection on Dyck Paths and its Cycle Structure
|
2007
|
David Callan
|
|
+
|
Cesaro's integral formula for the Bell numbers (corrected)
|
2007
|
David Callan
|
|
+
|
A combinatorial interpretation for the identity Sum_{k=0}^{n} binom{n}{k} Sum_{j=0}^{k} binom{k}{j}^{3}= Sum_{k=0}^{n} binom{n}{k}^{2}binom{2k}{k}
|
2007
|
David Callan
|
|
+
|
Bijections from Dyck paths to 321-avoiding permutations revisited
|
2007
|
David Callan
|
|
+
|
A determinant of Stirling cycle numbers counts unlabeled acyclic single-source automata
|
2007
|
David Callan
|
|
+
|
Sets, Lists and Noncrossing Partitions
|
2007
|
David Callan
|
|
+
|
The Maximum Associativeness of Division: 11091
|
2006
|
David Callan
|
|
+
|
A Combinatorial Interpretation of j/n {kn}\choose{n+j}
|
2006
|
David Callan
|
|
+
|
Permutations avoiding a nonconsecutive instance of a 2- or 3-letter pattern
|
2006
|
David Callan
|
|
+
|
Sierpinski's triangle and the Prouhet-Thue-Morse word
|
2006
|
David Callan
|
|
+
|
A bijection on Dyck paths and its cycle structure
|
2006
|
David Callan
|
|
+
|
The 136th manifestation of C_n
|
2005
|
David Callan
|
|
+
|
On conjugates for integer compositions and set partitions
|
2005
|
David Callan
|
|
+
|
A combinatorial interpretation of the eigensequence for composition
|
2005
|
David Callan
|
|
+
|
A combinatorial interpretation for a super-Catalan recurrence.
|
2005
|
David Callan
|
|
+
|
Some identities for the Catalan and Fine numbers
|
2005
|
David Callan
|
|
+
|
A Wilf equivalence related to two stack sortable permutations
|
2005
|
David Callan
|
|
+
|
On conjugates for set partitions and integer compositions
|
2005
|
David Callan
|
|
+
|
Noncrossing partitions under rotation and reflection
|
2005
|
David Callan
Len Smiley
|
|
+
|
Some bijections and identities for the Catalan and Fine numbers.
|
2005
|
David Callan
|
|
+
|
A combinatorial interpretation of the eigensequence for composition
|
2005
|
David Callan
|
|
+
PDF
Chat
|
A Uniformly Distributed Statistic on a Class of Lattice Paths
|
2004
|
David Callan
|
|
+
|
Bijections from restricted Dyck paths to Motzkin paths
|
2004
|
David Callan
|
|
+
PDF
Chat
|
A Combinatorial Proof of Sun's "Curious" Identity
|
2004
|
David Callan
|
|
+
|
A combinatorial proof of Sun's
|
2004
|
David Callan
|
|
+
|
A combinatorial proof of Sun's "curious" identity
|
2004
|
David Callan
|
|
+
|
Some bijections for restricted Motzkin paths
|
2004
|
David Callan
|
|
+
|
Two Bijections for Dyck Path Parameters
|
2004
|
David Callan
|
|
+
|
A combinatorial interpretation for a super-Catalan recurrence
|
2004
|
David Callan
|
|
+
|
A combinatorial proof of Sun's “curious” identity.
|
2004
|
David Callan
|
|
+
|
A Combinatorial Derivation of the Number of Labeled Forests
|
2003
|
David Callan
|
|
+
|
Another Description of the Central Delannoy Numbers: 10894
|
2003
|
Robert Sulanke
José Luis Arregui
Danijela Vujic
Nelson Castaneda
David Callan
|
|
+
|
Another Binomial Coefficient Identity: 10878
|
2003
|
Pal Peter Dalyay
S. Amghibech
David Callan
|
|
+
|
Counting stabilized-interval-free permutations
|
2003
|
David Callan
|
|
+
|
A uniformly distributed parameter on a class of lattice paths
|
2003
|
David Callan
|
|
+
|
A combinatorial derivation of the number of labeled forests
|
2003
|
David Callan
|
|
+
|
A Property of the Binary Sum of a Family of Sets: 10865
|
2002
|
David Beckwith
Li Zhou
David Callan
|
|
+
|
A Recursively Defined Sequence of Functions: 10785
|
2002
|
Emeric Deutsch
John Henry Steelman
David Callan
|
|
+
|
Pattern avoidance in circular permutations
|
2002
|
David Callan
|
|
+
|
Jordan and Smith forms of Pascal-related matrices
|
2002
|
David Callan
|
|
+
|
A recursive bijective approach to counting permutations containing 3-letter patterns
|
2002
|
David Callan
|
|
+
|
Another Path to Generalized Catalan Numbers: 10751
|
2001
|
Emeric Deutsch
David Callan
Sabin Cautis
Southwest Missouri Problems Group
|
|
+
|
A Rational Generating Function for Relative Divisors: 10750
|
2001
|
Leonard M. Smiley
David Callan
David M. Wells
S. Amghibech
|
|
+
|
Permutations and Coin-Tossing Sequences
|
2001
|
David Callan
|
|
+
|
A Generalization of Hall's Theorem: 10701
|
2001
|
Fred Galvin
Stephen C. Locke
Sung‐Soo Kim
David Callan
|
|
+
|
Permutation Parameters with the Same Distribution: 10634
|
2000
|
Emeric Deutsch
Ira M. Gessel
David Callan
|
|
+
|
Another Type of Lattice Path: 10658
|
2000
|
Emeric Deutsch
David Callan
Matthias Beck
D. Beckwith
Walter Böhm
R. F. McCoart
GCHQ Problems Group
|
|
+
|
A Sum of Chebyshev Inequalities: 10687
|
2000
|
James C. Owings
Jeremy E. Dawson
Robin Chapman
Darryl K. Nester
Robert A. Agnew
John Beebee
David Callan
Ricardo Garcı́a-Pelayo
Verónica Hernández
Joaquim Martı́n
|
|
+
|
A Recurrence Generating Multiples of Primes: 10655
|
2000
|
Mihály Bencze
Dan Saracino
Allen Stenger
S. Amghibech
Jean Anglesio
Rudolf Bauer
Andrew F. Siegel
D. M. Bloom
G. L. Body
David Callan
|
|
+
|
When a Multiple of π/2 is Close to an Integer: 10640
|
2000
|
Michael Filaseta
Allen Stenger
David Callan
Zachary Franco
|
|
+
|
The eigenvectors of the right-justified Pascal triangle
|
2000
|
David Callan
|
|
+
|
Rogers-Ramanujan Partitions: 10627
|
2000
|
George E. Andrews
John Henry Steelman
G. L. Body
David Callan
Robin Chapman
KA-SING LAU
James T. Lewis
John H. Lindsey
Graham Lord
James G. Merickel
|
|
+
|
Partitions and Pentagonal Numbers: 10628
|
2000
|
George E. Andrews
Kee-Wai Lau
G. L. Body
David Callan
Rebecca Chapman
Graham Lord
Heinz-Jürgen Seiffert
Doron Zeilberger
|
|
+
|
Two Uniformly Distributed Parameters Defining Catalan Numbers
|
1999
|
David Callan
|
|
+
|
Two Uniformly Distributed Parameters Defining Catalan Numbers
|
1999
|
David Callan
|
|
+
|
A Combinatorial Interpretation of a Catalan Numbers Identity
|
1999
|
David Callan
|
|
+
|
A Combinatorial Interpretation of a Catalan Numbers Identity
|
1999
|
David Callan
|
|
+
|
On a Convolution of Eulerian Numbers: 10609
|
1999
|
Donald E. Knuth
David Callan
|
|
+
|
Mobius Function on the Partition Lattice: 10506
|
1998
|
David Callan
Richard Stong
|
|
+
|
When Does m-n Divide f(m)-f(n)? A Look at Column-Finite Matrices
|
1997
|
David Callan
|
|
+
|
An Exploratory Approach to Kaplansky's Lemma Leads to a Generalized Resultant
|
1997
|
David Callan
|
|
+
|
An Exploratory Approach to Kaplansky's Lemma Leads to a Generalized Resultant
|
1997
|
David Callan
|
|
+
|
Research problem
|
1995
|
David Callan
|
|
+
|
On evaluating permanents and a matrix of contangents<sup>∗</sup>
|
1995
|
David Callan
|
|
+
|
A Possible Permanent Formula
|
1994
|
David Callan
|
|
+
|
A Possible Permanent Formula
|
1994
|
David Callan
|
|
+
|
Another determinant condensation formula
|
1991
|
David Callan
|
|
+
|
The isomorphisms of unitary groups over noncommutative domains
|
1978
|
David Callan
|
|
+
|
The generation of Sp(F2) by transvections
|
1976
|
David Callan
|