James A. Sellers

collaborators

5 papers

math.CO2026

A Family of Congruences Modulo 7 for Partitions with Monochromatic Even Parts and Multi--Colored Odd Parts

Michael D. Hirschhorn, James A. Sellers

In recent work, Amdeberhan and Merca considered the integer partition function $a (n)$ which counts the number of integer partitions of weight $n$ wherein even parts come in only on…

math.CO2026

Arithmetic Properties of Colored Partitions Restricted by Parity of the Parts

M. P. Thejitha, James A. Sellers, S. N. Fathima

Let $a_{r, s} (n)$ denote the number of mutlicolored partitions of $n$ , wherein both even parts and odd parts may appear in one of $r$ -colors and $s$ -colors, respectively, for fixed…

math.NT2026

Additional Congruences for generalized Color Partitions of Hirschhorn and Sellers

Anjelin Mariya Johnson, James A. Sellers, S. N. Fathima

Let $a_{k} (n)$ denote the number of partitions of $n$ wherein even parts come in only one color, while the odd parts may be ``colored" with one of $k$ colors, for fixed $k$ . In this…

math.NT2025

Elementary Proofs and Generalizations of Recent Congruences of Thejitha and Fathima

James A. Sellers

Motivated by recent work of Hirschhorn and the author, Thejitha and Fathima recently considered arithmetic properties satisfied by the function $a_{5} (n)$ which counts the number of…

math.NT2025

Elementary Proofs of Two Congruences for Partitions with Odd Parts Repeated at Most Twice

James A. Sellers

In a recent article on overpartitions, Merca considered the auxiliary function $a (n)$ which counts the number of partitions of $n$ where odd parts are repeated at most twice (and t…