New congruences for broken $k$-diamond partitions

TL;DR

This paper introduces new infinite families of congruences related to broken k-diamond partitions, expanding the understanding of their arithmetic properties and modular behavior.

Contribution

The paper establishes novel infinite families of congruences for broken k-diamond partition functions, advancing the theoretical framework of partition congruences.

Findings

New infinite congruence families for broken k-diamond partitions

Enhanced understanding of partition congruence structures

Potential implications for modular forms and combinatorics

Abstract

The notion of broken $k$-diamond partitions was introduced by Andrews and Paule. Let $\Delta_{k}(n)$ denote the number of broken $k$-diamond partitions of $n$ for a fixed positive integer $k$. In this paper, we establish new infinite families of broken $k$-diamond partition congruences.