Results on some partition functions arising from certain relations involving the Rogers-Ramanujan continued fractions

TL;DR

This paper explores relations among Rogers-Ramanujan continued fractions to derive new generating functions and congruences modulo 5 and 25 for various partition functions, advancing understanding in partition theory.

Contribution

It introduces novel relations involving Rogers-Ramanujan continued fractions to obtain new generating functions and congruences for specific partition functions.

Findings

Derived new generating functions for partition functions.

Established congruences modulo 5 and 25 for 3-core, 4-core, 4-regular, and colored partitions.

Connected Rogers-Ramanujan continued fractions to partition congruences.

Abstract

Relations involving the Rogers-Ramanujan continued fractions $R(q),$ $R(q^3 ),$ and $R(q^4)$ are used to find new generating functions and congruences modulo 5 and 25 for 3-core, 4-core, 4-regular, and colored partition functions.