Unlimited parity alternating partitions

Abstract

We introduce a new type of partition 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. 

Key words: Partitions, unlimited parity alternating partitions, asymptotics, Ingham’s Tauberian theorem.