31 citations · 95 across the 24 of their papers we have counts for
10 papers · 1 filter
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…
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…
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…
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 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…
Unique path partitions: Characterization and Congruences
Christine Bessenrodt, Jørn B. Olsson, James A. Sellers
We give a complete classification of the unique path partitions and study congruence properties of the function which enumerates such partitions.
On Non-Squashing Partitions
N. J. A. Sloane, James A. Sellers
A partition n = p_1 + p_2 + ... + p_k with 1 <= p_1 <= p_2 <= ... <= p_k is called non-squashing if p_1 + ... + p_j <= p_{j+1} for 1 <= j <= k-1. Hirschhorn and Sellers showed that…