Hook-Length Biases in $t$-regular partitions
Combinatorics
2026-01-12 v1 Number Theory
Abstract
Recently, there has been a lot of work on combinatorial inequalities related to hook-lengths in -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 -regular partitions with certain distinct parts partitions.
Keywords
Cite
@article{arxiv.2601.05592,
title = {Hook-Length Biases in $t$-regular partitions},
author = {Manjil P. Saikia and Prabal Talukdar},
journal= {arXiv preprint arXiv:2601.05592},
year = {2026}
}
Comments
9 pages, accepted for publication in Enumerative Combinatorics and Applications