Ramanujan-type congruences for $2$-color partition triples

TL;DR

This paper establishes new Ramanujan-type congruences for the function counting 2-color partition triples with a restriction on one color, expanding the understanding of partition congruences.

Contribution

It introduces novel Ramanujan-type congruences for the partition function ${p}_{3,3}(n)$ involving 2-color triples with a divisibility restriction.

Findings

Derived Ramanujan-type congruences for ${p}_{3,3}(n)$

Extended classical partition congruence results to colored partitions

Provided new modular relations for partition counting functions

Abstract

Let ${p}_{3,3}(n)$ denote the number of $2$-color partition triples of $n$ where one of the colors appears only in parts that are multiples of $3$. In this paper, we shall establish some interesting Ramanujan-type congruences for ${p}_{3,3}(n)$.