Unlimited parity alternating partitions

TL;DR

This paper introduces a new class of partitions with alternating parity parts, analyzes their properties, and determines their asymptotic behavior using advanced mathematical techniques.

Contribution

It defines and studies a novel type of partitions with alternating parity, providing new insights and asymptotic formulas for their enumeration.

Findings

Derived the asymptotic behavior of the partition function

Established properties of parity alternating partitions

Applied Ingham's Tauberian theorem successfully

Abstract

We introduce a new type of partitions that consists of partitions whose different parts alternate in parity (e.g., $3+2+2+1+1$). Various properties of this partition function are studied. In particular, we obtain its asymptotic behavior by employing Ingham's Tauberian theorem.