Congruences for the number of partitions and bipartitions with distinct even parts

TL;DR

This paper establishes infinite families of congruences modulo 8 for the number of partitions with distinct even parts and bipartitions with similar restrictions, advancing understanding of their arithmetic properties.

Contribution

It introduces new infinite families of congruences modulo 8 for partition functions with specific parity restrictions, expanding the theory of partition congruences.

Findings

Infinite families of congruences for $ped(n)$ modulo 8.

Detailed analysis of $ped_{-2}(n)$ modulo 8.

Congruences for $ped_{2}(n)$ modulo 8.

Abstract

Let $ped(n)$ denote the number of partitions of $n$ wherein even parts are distinct (and odd parts are unrestricted). We show infinite families of congruences for $ped(n)$ modulo $8$. We also examine the behavior of $ped_{-2}(n)$ modulo $8$ in detail where $ped_{-2}(n)$ denotes the number of bipartitions of $n$ with even parts distinct. As a result, we find infinite families of congruences for $ped_{2}(n)$ modulo $8$.