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arXiv · 2502.12394

Fixed perimeter analogues of some partition results

Gabriel Gray·Emily Payne·Holly Swisher·Ren Watson
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Abstract

Euler's partition identity states that the number of partitions of $n$ into odd parts is equal to the number of partitions of $n$ into distinct parts. Strikingly, Straub proved in 2016 that this identity also holds when counting partitions of any size with largest hook (perimeter) $n$. This has inspired further investigation of partition identities and inequalities in the fixed perimeter setting. Here, we explore fixed perimeter analogues of some well-known partition results inspired by Euler's partition identity.

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Gabriel Gray, Emily Payne, Holly Swisher, Ren Watson. 2025-02-18. Fixed perimeter analogues of some partition results. https://arxiv.org/abs/2502.12394

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