A curious identity and its applications to partitions with bounded part differences

TL;DR

This paper introduces a novel q-series identity and explores its applications to partitions where the difference between parts is bounded, providing new insights into partition theory.

Contribution

The paper presents a new q-series identity and applies it to analyze partitions with bounded part differences, offering novel theoretical tools.

Findings

Derived a new q-series identity

Applied the identity to partitions with bounded differences

Enhanced understanding of partition structures

Abstract

In this note, we present a curious $q$-series identity with applications to certain partitions with bounded part differences.