Separable integer partition classes with restrictions on consecutive parts

2025/08/15 by Chen, Y. Q., He, Thomas Y., Huang, X. M. +1
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.11766

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.

Citations

• Six types of separable integer partitions
• Separable overpartition classes and the r-chain excludant sizes of an overpartition
• Overpartitions with separated overlined parts and non-overlined parts
• Separable integer partition classes and partitions with congruence conditions
• Some Separable integer partition classes
• Separable Integer Partition Classes

Related

• Six types of separable integer partitions
• Separable Integer Partition Classes
• Some Separable integer partition classes
• Partitions in which every term but the smallest one is consecutive
• Generalization of a few results in Integer Partitions