Even-Odd partition identities of Rogers-Ramanujan type

TL;DR

This paper introduces new Rogers-Ramanujan type partition identities involving distinct constraints on even and odd parts, expanding the classical set of identities with broader combinatorial interpretations.

Contribution

The paper proves a new Rogers-Ramanujan type identity and generalizes it to two families of identities with novel partition constraints.

Findings

New Rogers-Ramanujan type identity proved.

Two families of generalized identities established.

Partitions with specific even-odd constraints characterized.

Abstract

We prove a theorem which add a new member to Rogers-Ramanujan identities. This new member counts partitions with different type of constraints on even and odd parts. Generalizing this theorem, we obtain two family of partition identities of Rogers-Ramanujan type.