Combinatorial interpretations of two identities of Guo and Yang

TL;DR

This paper offers new combinatorial interpretations of two identities by Guo and Yang, using a novel class of restricted partitions into parts of two kinds, extending previous work on partitions with bounded largest part and number of parts.

Contribution

It introduces a new class of restricted partitions into parts of two kinds to interpret two identities of Guo and Yang, advancing combinatorial understanding.

Findings

Provided combinatorial interpretations for Guo and Yang's identities.

Extended the concept of restricted partitions to parts of two kinds.

Enhanced the combinatorial framework for partition identities.

Abstract

The restricted partitions in which the largest part is less than or equal to $N$ and the number of parts is less than or equal to $k$ were investigated by Andrews in \cite{Andrews76}. These partitions were extended recently by the author to the partitions into parts of two kinds. In this paper, we use a new class of restricted partitions into parts of two kinds to provide new combinatorial interpretations for two identities of Guo and Yang.