Hook-Length Biases in $t$-regular partitions
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866911363111059456 |
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| author | Saikia, Manjil P. Talukdar, Prabal |
| author_facet | Saikia, Manjil P. Talukdar, Prabal |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_05592 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Hook-Length Biases in $t$-regular partitions Saikia, Manjil P. Talukdar, Prabal Combinatorics Number Theory 11P82, 05A15, 05A17, 05A19 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. |
| title | Hook-Length Biases in $t$-regular partitions |
| topic | Combinatorics Number Theory 11P82, 05A15, 05A17, 05A19 |
| url | https://arxiv.org/abs/2601.05592 |