A bijective look at gapfree partitions: between local and global

期刊论文
发表日期：

2025年4月15日

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Shane Chern,
Shishuo Fu,
Dazhao Tang

摘要

The mock theta function $\sigma ^*(q)$ $σ^{*} (q)$ first considered by Andrews, Dyson and Hickerson enumerates the set of gapfree partitions into odd parts, bearing a global nature. It is also known that the series $\sigma ^*(q)$ $σ^{*} (q)$ is related to the maximal excludant statistic for unrestricted partitions, which characterizes the gapfree condition locally. In this paper, we connect the two partition interpretations from a bijective perspective.