On congruence conjectures of Andrews and Bachraoui

TL;DR

This paper proves conjectures related to Ramanujan-type congruences and vanishing identities for restricted two-color partitions by connecting generating functions to modular forms and mock theta functions.

Contribution

It resolves two conjectures by relating generating functions to modular forms and mock theta functions, advancing understanding of partition congruences.

Findings

Confirmed conjectures on Ramanujan-type congruences.

Established a vanishing identity for the limiting sequence.

Linked generating functions to modular forms and mock theta functions.

Abstract

Andrews and the third author recently studied congruences for certain restricted two-color partitions. They made two conjectures for Ramanujan-type congruences and a vanishing identity for the limiting sequence. In this paper, we settle these conjectures by relating the corresponding generating function to modular forms and mock theta functions.