M_2-rank differences for partitions without repeated odd parts

TL;DR

This paper derives formulas for the generating functions of M_2-rank differences in partitions without repeated odd parts, utilizing modular forms and Lambert series.

Contribution

It provides new explicit formulas for M_2-rank differences in a specific class of partitions, connecting them with modular forms and Lambert series.

Findings

Formulas for M_2-rank differences are expressed in terms of modular forms.

Generated functions are linked to generalized Lambert series.

Results enhance understanding of partition rank statistics.

Abstract

We prove formulas for the generating functions for M_2-rank differences for partitions without repeated odd parts. These formulas are in terms of modular forms and generalized Lambert series.