31 citations · 95 across the 24 of their papers we have counts for
18 papers · 1 filter
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…
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…
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…
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…
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…
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…
Congruences for the Fishburn Numbers
George E. Andrews, James A. Sellers
The Fishburn numbers, are defined by a formal power series expansion For half of the prim…
Congruences for Generalized Frobenius Partitions with an Arbitrarily Large Number of Colors
Frank G. Garvan, James A. Sellers
In his 1984 AMS Memoir, George Andrews defined the family of --colored generalized Frobenius partition functions. These are denoted by where is the number of…
An Unexpected Congruence Modulo 5 for 4--Colored Generalized Frobenius Partitions
James A. Sellers
In his 1984 AMS Memoir, George Andrews defined the family of --colored generalized Frobenius partition functions. These are denoted by where is the number of…