On the biases and asymptotics of partitions with finite choices of parts
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911169825996800 |
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| author | Li, Jiyou Zhao, Sicheng |
| author_facet | Li, Jiyou Zhao, Sicheng |
| contents | Biases in integer partitions have been studied recently. For three disjoint subsets $R,S,I$ of positive integers, let $p_{RSI}(n)$ be the number of partitions of $n$ with parts from $R\cup S\cup I$ and $p_{R>S,I}(n)$ be the number of such partitions with more parts from $R$ than that from $S$. In this paper, in the case that $R,S,I$ are finite we obtain a concrete formula of the asymptotic ratio of $p_{R>S,I}(n)$ to $p_{RSI}(n)$. We also propose a conjecture in the case that $R,S$ are certain infinite arithmetic progressions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_04588 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the biases and asymptotics of partitions with finite choices of parts Li, Jiyou Zhao, Sicheng Combinatorics 05A17 11P81 Biases in integer partitions have been studied recently. For three disjoint subsets $R,S,I$ of positive integers, let $p_{RSI}(n)$ be the number of partitions of $n$ with parts from $R\cup S\cup I$ and $p_{R>S,I}(n)$ be the number of such partitions with more parts from $R$ than that from $S$. In this paper, in the case that $R,S,I$ are finite we obtain a concrete formula of the asymptotic ratio of $p_{R>S,I}(n)$ to $p_{RSI}(n)$. We also propose a conjecture in the case that $R,S$ are certain infinite arithmetic progressions. |
| title | On the biases and asymptotics of partitions with finite choices of parts |
| topic | Combinatorics 05A17 11P81 |
| url | https://arxiv.org/abs/2404.04588 |