31 citations · 95 across the 24 of their papers we have counts for
29 papers
Elementary Proofs of Congruences for POND and PEND Partitions
James A. Sellers
Recently, Ballantine and Welch considered various generalizations and refinements of POD and PED partitions. These are integer partitions wherein the odd parts must be distinct (in…
Elementary Proofs of Arithmetic Properties for Schur-Type Overpartitions Modulo Small Powers of 2
Shane Chern, Robson da Silva, James A. Sellers
In 2022, Broudy and Lovejoy extensively studied the function which counts the number of overpartitions of \emph{Schur-type}. In particular, they proved a number of congruenc…
An infinite family of internal congruences modulo powers of 2 for partitions into odd parts with designated summands
Shane Chern, James A. Sellers
In 2002, Andrews, Lewis, and Lovejoy introduced the combinatorial objects which they called \emph{partitions with designated summands}. These are built by taking unrestricted integ…
An Elementary Proof of a Conjecture of Saikia on Congruences for --Colored Overpartitions
James A. Sellers
The starting point for this work is the family of functions which counts the number of --colored overpartitions of In recent years, several infinite…
d-Fold Partition Diamonds
Dalen Dockery, Marie Jameson, James A. Sellers +1
In this work we introduce new combinatorial objects called --fold partition diamonds, which generalize both the classical partition function and the partition diamonds of Andrew…
New Infinite Families of Congruences Modulo Powers of 2 for 2--Regular Partitions with Designated Summands
James A. Sellers
In 2002, Andrews, Lewis, and Lovejoy introduced the combinatorial objects which they called {\it partitions with designated summands}. These are built by taking unrestricted intege…
On Blecher and Knopfmacher's Fixed Points for Integer Partitions
Brian Hopkins, James A. Sellers
Recently, Blecher and Knopfmacher explored the notion of fixed points in integer partitions and hypothesized on the relative number of partitions with and without a fixed point. We…
Elementary Proofs of Infinite Families of Congruences for Merca's Cubic Partitions
Robson da Silva, James A. Sellers
Recently, using modular forms and Smoot's {\tt Mathematica} implementation of Radu's algorithm for proving partition congruences, Merca proved the following two congruences: For al…
On the Divisibility of 7-Elongated Plane Partition Diamonds by Powers of 8
James A. Sellers, Nicolas Allen Smoot
In 2021 da Silva, Hirschhorn, and Sellers studied a wide variety of congruences for the -elongated plane partition function by various primes. They also conjectured the…
On the Parity of the Generalized Frobenius Partition Functions
George E. Andrews, James A. Sellers, Fares Soufan
In his 1984 Memoir of the American Mathematical Society, George Andrews defined two families of functions, and which enumerate two types of combinatorial object…
Elementary Proofs of Infinitely Many Congruences for -Elongated Partition Diamonds
Robson da Silva, Michael D. Hirschhorn, James A. Sellers
In 2007, Andrews and Paule published the eleventh paper in their series on MacMahon's partition analysis, with a particular focus on broken -diamond partitions. On the way to br…
Partitions Associated to Class Groups of Imaginary Quadratic Number Fields
Kathleen Petersen, James Sellers
We investigate properties of attainable partitions of integers, where a partition of is attainable if . Conjecturally, under an ex…
Combinatorial Perspectives on the Crank and Mex Partition Statistics
Brian Hopkins, James A. Sellers, Ae Ja Yee
Several authors have recently considered the smallest positive part missing from an integer partition, known as the minimum excludant or mex. In this work, we revisit and extend co…
Dyson's Crank and the Mex of Integer Partitions
Brian Hopkins, James A. Sellers, Dennis Stanton
Andrews and Newman have recently introduced the notion of the mex of a partition, the smallest positive integer that is not a part. The concept has been used since at least 2011, t…
Congruences for the coefficients of the Gordon and McIntosh mock theta function
Robson da Silva, James A. Sellers
Recently Gordon and McIntosh introduced the third order mock theta function defined by Our g…
Parity Considerations for Mex-Related Partition Functions of Andrews and Newman
Robson da Silva, James A. Sellers
In a recent paper, Andrews and Newman extended the mex-function to integer partitions and proved many partition identities connected with these functions. In this paper, we present…
On the parity of the number of partitions with odd multiplicities
James A. Sellers, Fabrizio Zanello
Recently, Hirschhorn and the first author considered the parity of the function which counts the number of integer partitions of wherein each part appears with odd multi…
Sequentially congruent partitions and partitions into squares
Robert Schneider, James A. Sellers, Ian Wagner
In recent work, M. Schneider and the first author studied a curious class of integer partitions called "sequentially congruent" partitions: the th part is congruent to the $(m+1…
Simultaneous core partitions with nontrivial common divisor
Jean-Baptiste Gramain, Rishi Nath, James A. Sellers
A tremendous amount of research has been done in the last two decades on -core partitions when and are positive integers with no common divisor. Here we change persp…
Abaci structures of -core partitions
Rishi Nath, James A. Sellers
We develop a geometric approach to the study of -core and -core partitions through the associated -abaci. This perspective yields new proofs for results of…
A periodic approach to plane partition congruences
Matthew S. Mizuhara, James A. Sellers, Holly Swisher
Ramanujan's celebrated congruences of the partition function have inspired a vast amount of results on various partition functions. Kwong's work on periodicity of rational p…
A combinatorial proof of a relationship between maximal and -cores
Rishi Nath, James A. Sellers
Integer partitions which are simultaneously --cores for distinct values of have attracted significant interest in recent years. When and are relatively prime, Olsson…
Congruences for spin characters of the double covers of the symmetric and alternating groups
Rishi Nath, James A. Sellers
Let be an odd prime. The bar partitions with sign and -bar-core partitions with sign respectively label the spin characters and -defect zero spin characters of the double…
Arithmetic Properties of Andrews' Singular Overpartitions
Shi-Chao Chen, Michael D. Hirschhorn, James A. Sellers
In a very recent work, G. E. Andrews defined the combinatorial objects which he called {\it singular overpartitions} with the goal of presenting a general theorem for overpartition…