Separable integer partition classes with restrictions on consecutive parts

TL;DR

This paper explores a specific class of integer partitions with restrictions on consecutive parts, demonstrating their separability and providing generating functions, thereby extending the theory of separable integer partition classes.

Contribution

It introduces and analyzes partitions with restrictions on consecutive parts, proving they form separable classes and deriving their generating functions.

Findings

Partitions with restrictions on consecutive parts are separable integer partition classes.

Generated explicit formulas for the generating functions of these restricted partitions.

Extended the theory of separable integer partition classes to new types of partitions.

Abstract

Recently, Andrews introduced separable integer partition classes and studied some well-known theorems. In this article, we will consider the types of partitions with restrictions on consecutive parts. We will show that such partitions are separable integer partition classes and then give the generating functions for such partitions.