On the asymptotics of certain colored partitions

TL;DR

This paper establishes a series of asymptotic formulas for the logarithm of specific two-colored partitions, advancing understanding in partition theory and addressing a conjecture by Guadalupe.

Contribution

It proves an infinite family of asymptotic formulas for two-colored partitions, including a previously conjectured sub-family.

Findings

Derived new asymptotic formulas for two-colored partitions

Confirmed a conjecture by Guadalupe within this family

Enhanced theoretical understanding of partition asymptotics

Abstract

We will prove an infinite family of asymptotic formulas for the logarithm of certain two-colored partitions. An infinite sub-family of these asymptotics was posed as a conjecture by Guadalupe.