Andrew V. Sills

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All published works

Action	Title	Year	Authors
+ PDF Chat	On the $q$-factorization of power series	2025	Robert Schneider Andrew V. Sills Hunter Waldron
+ PDF Chat	"Overpartitionized" Rogers--Ramanujan type identities	2025	Abdulaziz Analazi Augustine O. Munagi Andrew V. Sills
+ PDF Chat	Composition-theoretic series and false theta functions	2024	William Keith Robert Schneider Andrew V. Sills
+ PDF Chat	A refinement of the multinomial distribution with application	2024	Andrew V. Sills
+ PDF Chat	Analysis and combinatorics of partition zeta functions	2024	Robert Schneider Andrew V. Sills
+ PDF Chat	Mathematics of the MML functional quantizer modules for VCV Rack software synthesizer	2024	Michael G. Maxwell Caroline McCarthy Joshua Pfeffer Maxwell Schneider Robert Schneider Andrew V. Sills
+ PDF Chat	On integer partitions and the Wilcoxon rank-sum statistic	2024	Andrew V. Sills
+	A Refinement of the Multinomial Distribution with Application	2024	Andrew V. Sills
+	Composition-theoretic series in partition theory	2023	Robert Schneider Andrew V. Sills
+	The Generalized Law of Total Covariance	2022	Charles W. Champ Andrew V. Sills
+	Process, Population, and Sample: the Researcher's Interest	2022	Charles W. Champ Andrew V. Sills
+	Combinatorial formulas for arithmetic density	2022	Robert Schneider Andrew V. Sills
+	Composition-theoretic series in partition theory	2022	Robert Schneider Andrew V. Sills
+	Derivation of Identities of the Rogers--Ramanujan Type by the Method of Constant Terms	2022	Andrew V. Sills
+ PDF Chat	A refinement of the binomial distribution using the quantum binomial theorem	2021	Andrew V. Sills
+	A q-analog of the binomial distribution	2020	Andrew V. Sills
+	A refinement of the binomial distribution using the quantum binomial theorem.	2020	Andrew V. Sills
+ PDF Chat	Analysis and combinatorics of partition zeta functions	2020	Robert Schneider Andrew V. Sills
+	A refinement of the binomial distribution using the quantum binomial theorem	2020	Andrew V. Sills
+	Towards an automation of the circle method	2020	Andrew V. Sills
+ PDF Chat	Integer partitions probability distributions	2019	Andrew V. Sills
+ PDF Chat	The Combinatorics of MacMahon’s Partial Fractions	2019	Andrew V. Sills
+ PDF Chat	The Combinatorics of MacMahon’s Partial Fractions	2019	Andrew V. Sills
+ PDF Chat	The exponential distribution analog of the Grubbs–Weaver method	2019	Andrew V. Sills Charles W. Champ
+	Finite Rogers--Ramanujan type identities	2019	Andrew V. Sills
+	Polynomial Generalizations of two-variable Ramanujan type identities	2019	James Mc Laughlin Andrew V. Sills
+	Hybrid Proofs of the $q$-Binomial Theorem and other identities	2019	Dennis Eichhorn James Mc Laughlin Andrew V. Sills
+	Rogers-Ramanujan-Slater Type Identities	2019	James Mc Laughlin Andrew V. Sills Peter Zimmer
+	The product of parts or "norm" of a partition	2019	Andrew V. Sills Robert Schneider
+	Finite Rogers--Ramanujan type identities	2019	Andrew V. Sills
+	Hybrid Proofs of the $q$-Binomial Theorem and other identities	2019	Dennis Eichhorn James Laughlin Andrew V. Sills
+	Polynomial Generalizations of two-variable Ramanujan type identities	2019	James Laughlin Andrew V. Sills
+	Rogers-Ramanujan-Slater Type Identities	2019	James Laughlin Andrew V. Sills Peter Zimmer
+	Some implications of Chu's $_{10}ψ_{10}$ extension of Bailey's $_{6}ψ_{6}$ summation formula	2019	James Laughlin Andrew V. Sills Peter Zimmer
+	Combinatorics of Ramanujan--Slater type identities	2018	James Mc Laughlin Andrew V. Sills
+	Partition Recurrences	2018	Yuriy Choliy Louis W. Kolitsch Andrew V. Sills
+	On the ordinary and signed Göllnitz--Gordon partitions	2018	Andrew V. Sills
+	Combinatorics of Ramanujan--Slater type identities	2018	James Laughlin Andrew V. Sills
+	Disturbing the $q$-Dyson Conjecture	2018	Andrew V. Sills
+	Odd Fibbinary Numbers and the Golden Ratio	2018	Linus Lindroos Andrew V. Sills Hua Wang
+	Motivated Proofs Connections to Lie Algebras, and More Identities	2017	Andrew V. Sills
+	Parts and Subword Patterns in Compositions	2017	Brian Hopkins Mark Shattuck Andrew V. Sills Thotsaporn Thanatipanonda Hua Wang
+	Rogers–Ramanujan Type Partition Identities	2017	Andrew V. Sills
+ PDF Chat	A Classical q-Hypergeometric Approach to the $$A_2^{(2)}$$ Standard Modules	2017	Andrew V. Sills
+	Ghost series and a motivated proof of the Andrews–Bressoud identities	2016	Shashank Kanade James Lepowsky Matthew C. Russell Andrew V. Sills
+ PDF Chat	A Formula for the Partition Function That “Counts”	2016	Yuriy Choliy Andrew V. Sills
+	Euler-Type Partition Recurrences	2016	Andrew V. Sills
+	Rogers–Ramanujan Type Identities	2015	Andrew V. Sills
+	MacMahon’s Partial Fractions	2015	Andrew V. Sills
+	Odd Fibbinary Numbers and the Golden Ratio	2014	Linus Lindroos Andrew V. Sills Hua Wang
+	Odd Fibbinary Numbers and the Golden Ratio	2014	Linus Lindroos Andrew V. Sills Hua Wang
+	A Rademacher Type Formula For Partitions and Overpartitions	2013	Andrew V. Sills
+	Compositions, Partitions, and Fibonacci Numbers	2013	Andrew V. Sills
+	The Minimal Number of Subtrees of a Tree	2013	Andrew V. Sills Hua Wang
+	Rademacher-type formulas for restricted partition and overpartition functions	2013	Andrew V. Sills
+	A Rademacher Type Formula For Partitions and Overpartitions	2013	Andrew V. Sills
+	Compositions, Partitions, and Fibonacci Numbers	2013	Andrew V. Sills
+ PDF Chat	On a Pair of Identities from Ramanujan's Lost Notebook	2012	James McLaughlin Andrew V. Sills
+ PDF Chat	Rademacher's infinite partial fraction conjecture is (almost certainly) false	2012	Andrew V. Sills Doron Zeilberger
+	On the maximal Wiener index and related questions	2012	Andrew V. Sills Hua Wang
+ PDF Chat	Formulæ for the number of partitions of n into at most m parts (using the quasi-polynomial ansatz)	2012	Andrew V. Sills Doron Zeilberger
+	A Generalization of the Euler-Glaisher Bijection	2012	Andrew V. Sills
+	Rademacher’s Inﬁnite Partial Fractions Conjecture	2012	Andrew V. Sills
+	The Selected Works of George E Andrews	2011	George E. Andrews Andrew V. Sills
+	Compositions, Partitions, and Fibonacci Numbers	2011	Andrew V. Sills
+	Lecture Hall Sequences, q-Series, and Asymmetric Partition Identities	2011	Sylvie Corteel Carla D. Savage Andrew V. Sills
+ PDF Chat	Polynomial Generalizations of Two-Variable Ramanujan Type Identities	2011	James McLaughlin Andrew V. Sills
+ PDF Chat	Hybrid Proofs of the $q$-Binomial Theorem and Other Identities	2011	Dennis Eichhorn James McLaughlin Andrew V. Sills
+	Some implications of Chu's 10 10 extension of Bailey's 6 6 summation formula	2011	James McLaughlin Andrew V. Sills Peter Zimmer
+	q-Series: 2011: an International Conference on q - series, Partitions, and Special Functions	2011	Andrew V. Sills Steven B. Damelin
+	Some implications of Chu’s $ {}_{10}\psi_{10} $ extension of Bailey’s $ {}_6\psi_6 $ summation formula	2010	James Mc Laughlin Andrew V. Sills Peter Zimmer
+	On an identity of Gessel and Stanton and the new little Göllnitz identities	2010	Carla D. Savage Andrew V. Sills
+	Rademacher-type formulas for restricted partition and overpartition functions	2010	Andrew V. Sills
+ PDF Chat	A Rademacher Type Formula for Partitions and Overpartitions	2010	Andrew V. Sills
+	Instances of Gordon's Partition Theorem Have Been Hiding in Slater's List!	2010	Andrew V. Sills
+	Maximizing the Wiener Index	2010	Andrew V. Sills Hua Wang
+	Supplemental Funding for q -Series: 2011: An International Conference on q - series, Partitions, and Special Functions	2010	Andrew V. Sills
+	Identities of the Ramanujun-Slater Type	2010	Andrew V. Sills
+ PDF Chat	Towards an automation of the circle method	2010	Andrew V. Sills
+	Some Implications of Chu's 10ψ10 Generalization of Bailey's 6ψ6 Summation Formula	2010	James McLaughlin Andrew V. Sills Peter Zimmer
+	Lifting Bailey pairs to WP-Bailey pairs	2009	James McLaughlin Andrew V. Sills Peter Zimmer
+ PDF Chat	Combinatorics of Ramanujan–Slater Type Identities	2009	James McLaughlin Andrew V. Sills
+	Rogers–Ramanujan computer searches	2009	James McLaughlin Andrew V. Sills Peter Zimmer
+	On the Rogers-Selberg Identities and Gordon’s Theorem	2009	Andrew V. Sills
+	Combinatorics of Ramanujan-Slater Type Identities	2009	James McLaughlin Andrew V. Sills
+ PDF Chat	Some more identities of the Rogers-Ramanujan type	2008	Douglas Bowman James Mc Laughlin Andrew V. Sills
+	Rogers-Ramanujan-Slater Type Identities	2008	James Mc Laughlin Andrew V. Sills Peter Zimmer
+ PDF Chat	Ramanujan–Slater type identities related to the moduli 18 and 24	2008	James McLaughlin Andrew V. Sills
+	A Generalization of the Euler-Glaisher Partition Bijection	2008	Andrew V. Sills James A. Sellers Gary L. Mullen
+	A Partition Bijection Relating the Rogers-Selberg Identities to a Special Case of Gordon’s Theorem	2008	Andrew V. Sills
+ PDF Chat	Disturbing the 𝑞-Dyson conjecture	2008	Andrew V. Sills
+	On the Ordinary and Signed Göllnitz-Gordon Partitions	2008	Andrew V. Sills
+ PDF Chat	IDENTITIES OF THE ROGERS–RAMANUJAN–SLATER TYPE	2007	Andrew V. Sills
+ PDF Chat	A partition bijection related to the Rogers–Selberg identities and Gordon's theorem	2007	Andrew V. Sills
+	Finding Polynomial Generalizations of q-Series Identities	2007	Andrew V. Sills
+	Polynomial Generalizations of q-Series Identities	2007	Andrew V. Sills
+	On Dyson’s q-Series Identities	2007	Andrew V. Sills
+ PDF Chat	On simplifications of certain q-multisums	2006	Andrew V. Sills
+	Some more identities of the Rogers-Ramanujan type	2006	Douglas Bowman James Mc Laughlin Andrew V. Sills
+ PDF Chat	On identities of the Rogers-Ramanujan type	2006	Andrew V. Sills
+ PDF Chat	Disturbing the Dyson conjecture, in a generally GOOD way	2006	Andrew V. Sills
+	Integer Partitions and Identities of Rogers-Ramanujan Type	2006	Andrew V. Sills
+ PDF Chat	Disturbing the Dyson Conjecture (in a GOOD Way)	2006	Andrew V. Sills Doron Zeilberger
+	Some more identities of the Rogers-Ramanujan type	2006	Douglas Bowman James Laughlin Andrew V. Sills
+ PDF Chat	Identities of the Rogers–Ramanujan–Bailey type	2005	Andrew V. Sills
+	Polynomial Generalizations of Rogers-Ramanujan Type Identities	2005	Andrew V. Sills
+	Multiparameter Bailey Pairs and Rogers-Ramanujan-Slater Identities	2005	Andrew V. Sills
+	Partitions of Integers	2005	Andrew V. Sills
+	Rogers-Ramanujan Type Identities and Partitions	2005	Andrew V. Sills
+ PDF Chat	<i>q</i>-Difference Equations and Identities of the Rogers–Ramanujan–Bailey Type	2004	Andrew V. Sills
+ PDF Chat	Bijections and Congruences for Generalizations of Partition Identities of Euler and Guy	2004	James A. Sellers Andrew V. Sills Gary L. Mullen
+	On series expansions of Capparelli's infinite product	2004	Andrew V. Sills
+ PDF Chat	A Combinatorial proof of a partition identity of Andrews and Stanley	2004	Andrew V. Sills
+	Rogers-Ramanujan-Bailey Identities	2004	Andrew V. Sills
+	Rogers-Ramanujan-Bailey Type Identities	2004	Andrew V. Sills
+	A Rogers-Ramanujan Computer Search	2004	Andrew V. Sills
+	RRtools—a Maple package for aiding the discovery and proof of finite Rogers–Ramanujan type identities	2003	Andrew V. Sills
+ PDF Chat	Finite Rogers-Ramanujan Type Identities	2003	Andrew V. Sills
+	Computer Algebra and Rogers-Ramanujan Type Identities	2003	Andrew V. Sills
+	Computer Algebra and Rogers-Ramanujan	2003	Andrew V. Sills
+	q-Pell sequences and two identities of V.A. Lebesgue	2002	José Plı́nio O. Santos Andrew V. Sills
+	Computer-assisted explorations of rogers-ramanujan type identities	2002	Andrew V. Sills George E. Andrews Avinash Sathaye
+	An Algorithmic Approach to Rogers-Ramanujan Type Identities	2002	Andrew V. Sills
+	Bijective Proofs for Some Equivalent Partition Ideals	2002	Andrew V. Sills
+	Rogers-Ramanujan Toolkit for Maple	2002	Andrew V. Sills
+	Connecting Collisions to Dynamical Evolution in Clusters	2002	Andrew V. Sills
+	The Colorful Combinatorics of Lebesgue’s Identity	2001	Andrew V. Sills
+	Computer Explorations of Rogers-Ramanujan Type Identities, Part 2	2001	Andrew V. Sills

Common Coauthors

Coauthor	Papers Together
James McLaughlin	10
Robert Schneider	9
James Mc Laughlin	8
Peter Zimmer	7
James Laughlin	6
Linus Lindroos	3
Charles W. Champ	3
Dennis Eichhorn	3
Douglas Bowman	3
Doron Zeilberger	3
Hua Wang	2
Yuriy Choliy	2
Hua Wang	2
Hua Wang	2
James A. Sellers	2
George E. Andrews	2
Peter Zimmer	2
Gary L. Mullen	2
Carla D. Savage	2
Michael G. Maxwell	1
Abdulaziz Analazi	1
José Plı́nio O. Santos	1
Steven B. Damelin	1
Maxwell Schneider	1
Augustine O. Munagi	1
Mark Shattuck	1
Sylvie Corteel	1
Louis W. Kolitsch	1
James Lepowsky	1
Caroline McCarthy	1
Joshua Pfeffer	1
Matthew C. Russell	1
Thotsaporn Thanatipanonda	1
William Keith	1
Avinash Sathaye	1
Shashank Kanade	1
Hunter Waldron	1
Hua Wang	1
Brian Hopkins	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+	Further Identities of the Rogers-Ramanujan Type	1952	Louise Slater	37
+	The Theory of Partitions	1984	George E. Andrews	29
+	Basic Hypergeometric Series	2004	George Gasper Mizan Rahman	21
+	On Two Theorems of Combinatory Analysis and Some Allied Identities	1917	L. J. Rogers	20
+	𝑞-Series: Their Development and Application in Analysis, Number Theory, Combinatorics, Physics and Computer Algebra	1986	George E. Andrews	19
+	Identities of the Rogers-Ramanujan Type	1948	W. N. Bailey	18
+	Some Identities in Combinatory Analysis	1946	W. N. Bailey	17
+	Ramanujan's Lost Notebook	2012	George E. Andrews Bruce C. Berndt	15
+ PDF Chat	Multiple series Rogers-Ramanujan type identities	1984	George E. Andrews	14
+ PDF Chat	IDENTITIES OF THE ROGERS–RAMANUJAN–SLATER TYPE	2007	Andrew V. Sills	14
+	Further Identities of the Rogers-Ramanujan Type	1952	L. J. Slater	13
+	A New Proof of Rogers's Transformations of Infinite Series	1951	Louise Slater	13
+	Ramanujan's Lost Notebook: Part II	2009	George E. Andrews Bruce C. Berndt	13
+ PDF Chat	On the q-analog of Kummer’s theorem and applications	1973	George E. Andrews	12
+	Some continued fractions of the Rogers-Ramanujan type	1965	Basil Gordon	11
+ PDF Chat	Asymptotic Formulaae in Combinatory Analysis	1918	G. H. Hardy S. Ramanujan	10
+	The lost notebook and other unpublished papers	1989	Srinivasa Ramanujan Aiyangar George E. Andrews	10
+	A Combinatorial Generalization of the Rogers-Ramanujan Identities	1961	Basil Gordon	10
+	Lattice gas generalization of the hard hexagon model. III.q-Trinomial coefficients	1987	George E. Andrews R. J. Baxter	9
+	Anti Self-Dual Yang-Mills Connections Over Complex Algebraic Surfaces and Stable Vector Bundles	1985	Simon Donaldson	9
+ PDF Chat	Finite Rogers-Ramanujan Type Identities	2003	Andrew V. Sills	9
+	RRtools—a Maple package for aiding the discovery and proof of finite Rogers–Ramanujan type identities	2003	Andrew V. Sills	8
+ PDF Chat	On identities of the Rogers-Ramanujan type	2006	Andrew V. Sills	8
+	An algorithmic proof theory for hypergeometric (ordinary and “q”) multisum/integral identities	1992	Herbert S. Wilf Doron Zeilberger	8
+	A New Proof of the Rogers-Ramanujan Identities	1929	G. N. Watson	8
+	Computer algebra and identities of the Rogers-Ramanujan type	1991	José Plı́nio O. Santos	8
+	A partition function connected with the modulus five	1941	Joseph Lehner	7
+ PDF Chat	Rational functions certify combinatorial identities	1990	Herbert S. Wilf Doron Zeilberger	7
+	Partitions Into Odd Summands	1963	Peter Hagis	7
+ PDF Chat	Applications of 𝑞-Lagrange inversion to basic hypergeometric series	1983	Ira M. Gessel Dennis Stanton	7
+	On the Simplification of Some Identities of the Rogers-Ramanujan Type	1951	W. N. Bailey	7
+	On the Partition Function <i>p</i> (<i>n</i> )	1938	Hans Rademacher	7
+	A generalization of the Rogers-Ramanujan identities for all moduli	1979	David M. Bressoud	7
+	Topics in Analytic Number Theory	1973	Hans Rademacher	7
+	Some identities for terminating q-series	1981	David M. Bressoud	6
+	THE QUINTUPLE PRODUCT IDENTITY	2006	S. Barry Cooper	6
+ PDF Chat	Polynomial identities, indices, and duality for theN=1 superconformal modelSM(2, 4v)	1996	Alexander Bérkovich Barry M. McCoy William P. Orrick	6
+	Short and Easy Computer Proofs of the Rogers-Ramanujan Identities and of Identities of Similar Type	1994	Peter Paule	6
+	An algebraic identity of F.H. Jackson and its implications for partitions	2001	George E. Andrews Richard P. Lewis	6
+	Gordon's theorem for overpartitions	2003	Jeremy Lovejoy	6
+ PDF Chat	Rogers-Schur-Ramanujan Type Identities for the M ( p , p ′) Minimal Models of Conformal Field Theory	1998	Alexander Bérkovich Barry M. McCoy Anne Schilling	6
+	qMultiSum—a package for proving q-hypergeometric multiple summation identities	2003	Axel Riese	6
+	Eight-vertex SOS model and generalized Rogers-Ramanujan-type identities	1984	George E. Andrews R. J. Baxter Peter J. Forrester	6
+	An Analytic Generalization of the Rogers-Ramanujan Identities for Odd Moduli	1974	George E. Andrews	6
+	�ber Partitionen mit Differenzenbedingungen	1954	G�nter Meinardus	6
+	Ramanujan’s Lost Notebook	2005	George E. Andrews Bruce C. Berndt	6
+	On a class of partitions with distinct summands	1964	Peter Hagis	5
+	Partitions in Certain Arithmetic Progressions	1961	Shô Iseki	5
+	Analytic and combinatorial generalizations of the Rogers-Ramanujan identities	1980	David M. Bressoud	5
+ PDF Chat	A Construction of the Level 3 Modules for the Affine Lie Algebra 𝐴₂⁽²⁾ and a New Combinatorial Identity of the Rogers-Ramanujan Type	1996	Stefano Capparelli	5