Hook length biases for self-conjugate partitions and partitions with distinct odd parts
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929400717508608 |
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| author | Cossaboom, Catherine |
| author_facet | Cossaboom, Catherine |
| contents | We establish a hook length bias between self-conjugate partitions and partitions of distinct odd parts, demonstrating that there are more hooks of fixed length $t \geq 2$ among self-conjugate partitions of $n$ than among partitions of distinct odd parts of $n$ for sufficiently large $n$. More precisely, we derive asymptotic formulas for the total number of hooks of fixed length $t$ in both classes. This resolves a conjecture of Ballantine, Burson, Craig, Folsom, and Wen. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_18480 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hook length biases for self-conjugate partitions and partitions with distinct odd parts Cossaboom, Catherine Combinatorics Number Theory We establish a hook length bias between self-conjugate partitions and partitions of distinct odd parts, demonstrating that there are more hooks of fixed length $t \geq 2$ among self-conjugate partitions of $n$ than among partitions of distinct odd parts of $n$ for sufficiently large $n$. More precisely, we derive asymptotic formulas for the total number of hooks of fixed length $t$ in both classes. This resolves a conjecture of Ballantine, Burson, Craig, Folsom, and Wen. |
| title | Hook length biases for self-conjugate partitions and partitions with distinct odd parts |
| topic | Combinatorics Number Theory |
| url | https://arxiv.org/abs/2406.18480 |