5 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…