Combinatorial proofs of the Ramanujan type congruences modulo 3

TL;DR

This paper introduces a new combinatorial approach using the $V_R$-rank to prove Ramanujan-type congruences modulo 3 for specific partition functions.

Contribution

It presents a novel combinatorial proof technique employing the $V_R$-rank to establish congruences, advancing understanding of partition function properties.

Findings

Proves Ramanujan-type congruences modulo 3 for certain partition classes

Introduces the $V_R$-rank as a combinatorial tool

Provides new combinatorial proofs for classical congruences

Abstract

The partition statistic $V_R$-rank is introduced to give combinatorial proofs of the Ramanujan type congruences mod 3 for certain classes of partition functions.