Modulo 2 congruences for partitions with initial repetitions

TL;DR

This paper explores parity formulas and Ramanujan-like congruences modulo 2 for partitions with initial repetitions, extending previous work on partition theory.

Contribution

It introduces new parity formulas and infinite families of modulo 2 congruences for a specific class of partitions with initial repetitions.

Findings

Derived parity formulas for partitions with initial repetitions

Established infinite families of Ramanujan-like congruences modulo 2

Extended the theory of partition congruences

Abstract

Motivated by Andrews' partitions with initial repetitions, we derive parity formulas for several functions for this class of partitions. In many cases, we present an infinite family of Ramanujan-like congruences modulo 2.