Congruences for the $k$ dots bracelet partition functions

TL;DR

This paper explores congruence relations between bracelet partition functions and regular partitions, deriving new modulo 2 congruences and analyzing their arithmetic properties modulo primes.

Contribution

It establishes new congruences for bracelet partition functions by relating them to regular partitions and studies their properties modulo primes.

Findings

Derived new modulo 2 congruences for 5 dots bracelet partitions.

Established relations between bracelet and regular partition generating functions.

Analyzed arithmetic properties of bracelet partitions modulo primes.

Abstract

By finding the congruent relations between the generating function of the 5 dots bracelet partitions and that of the 5-regular partitions, we get some new congruences modulo 2 for the 5 dots bracelet partition function. Moreover, for a given prime $p$, we study the arithmetic properties modulo $p$ of the $k$ dots bracelet partitions.