Parity results of PEND partition

TL;DR

This paper investigates the parity properties of a special class of integer partitions called PEND partitions, establishing infinite families of congruences modulo 2 through combinatorial and number-theoretic methods.

Contribution

It introduces new parity results for PEND partitions and proves infinite congruence families using Newman’s theorem.

Findings

Established infinite families of modulo 2 congruences for pend(n)

Connected PEND partitions to existing number-theoretic results

Extended understanding of partition parity properties

Abstract

In this paper, we consider the set of partitions $pend(n)$ which enumerates the number of partitions of $n$ wherein the even parts are not allowed to be distinct. Using a result of Newman, we prove a few infinite families of congruences modulo 2 for $pend(n)$.