Fixed perimeter analogues of some partition results

Authors

Gabriel Gray
Emily Payne, The University of Texas Rio Grande Valley
Holly Swisher
Ren Watson, University of Texas at Austin

Document Type

Article

Publication Date

5-2026

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 length (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.

Comments

Original published version available at https://doi.org/10.1016/j.disc.2025.114968

Recommended Citation

Gray, Gabriel, Emily Payne, Holly Swisher, and Ren Watson. "Fixed perimeter analogues of some partition results." Discrete Mathematics 349, no. 5 (2026): 114968. https://doi.org/10.1016/j.disc.2025.114968

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.

Publication Title

Discrete Mathematics

DOI

10.1016/j.disc.2025.114968