Proof of Singh and Barman's conjecture on hook length biases
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911275796135936 |
|---|---|
| author | Lin, Hongshu Zang, Wenston J. T. |
| author_facet | Lin, Hongshu Zang, Wenston J. T. |
| contents | Let $b_{t,i}(n)$ denote the total number of $i$-hooks in $t$-regular partitions of $n$. Singh and Barman conjectured that $b_{t+1,2}(n) \geq b_{t,2}(n)$ holds for all $t\ge 3$ and $n\ge 0$. This conjecture was known to hold for $t=3$ due to work of Barman Mahanta and Singh. In this paper, we prove this conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_19185 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Proof of Singh and Barman's conjecture on hook length biases Lin, Hongshu Zang, Wenston J. T. Combinatorics Let $b_{t,i}(n)$ denote the total number of $i$-hooks in $t$-regular partitions of $n$. Singh and Barman conjectured that $b_{t+1,2}(n) \geq b_{t,2}(n)$ holds for all $t\ge 3$ and $n\ge 0$. This conjecture was known to hold for $t=3$ due to work of Barman Mahanta and Singh. In this paper, we prove this conjecture. |
| title | Proof of Singh and Barman's conjecture on hook length biases |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2510.19185 |