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arXiv · 2601.05592

Hook-Length Biases in $t$-regular partitions

Manjil P. Saikia·Prabal Talukdar
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Abstract

Recently, there has been a lot of work on combinatorial inequalities related to hook-lengths in $t$-regular partitions. In this short note, we give a proof using generating functions for a result proved by Singh and Barman (2026) using combinatorial methods. In addition, we give an alternate proof of another result of Singh \& Barman (2024) which yields as a corollary a previously unobserved connection of hook-lengths in $t$-regular partitions with certain distinct parts partitions.

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Manjil P. Saikia, Prabal Talukdar. 2026-01-09. Hook-Length Biases in $t$-regular partitions. https://arxiv.org/abs/2601.05592

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