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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Online-Zugang: | https://arxiv.org/abs/2401.05874 |
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| _version_ | 1866909069635223552 |
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| author | Bringmann, Kathrin Franke, Johann Heim, Bernhard |
| author_facet | Bringmann, Kathrin Franke, Johann Heim, Bernhard |
| contents | Denote by $N_{\ell}(n)$ the number of $\ell$-tuples of elements in the symmetric group $S_n$ with commuting components, normalized by the order of $S_n$. In this paper, we prove asymptotic formulas for $N_\ell(n)$. In addition, general criteria for log-concavity are shown, which can be applied to $N_\ell(n)$ among other examples. Moreover, we obtain a Bessenrodt-Ono type theorem which gives an inequality of the form $c(a)c(b) > c(a+b)$ for certain families of sequences $c(n)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_05874 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Asymptotics of commuting $\ell$-tuples in symmetric groups and log-concavity Bringmann, Kathrin Franke, Johann Heim, Bernhard Number Theory Denote by $N_{\ell}(n)$ the number of $\ell$-tuples of elements in the symmetric group $S_n$ with commuting components, normalized by the order of $S_n$. In this paper, we prove asymptotic formulas for $N_\ell(n)$. In addition, general criteria for log-concavity are shown, which can be applied to $N_\ell(n)$ among other examples. Moreover, we obtain a Bessenrodt-Ono type theorem which gives an inequality of the form $c(a)c(b) > c(a+b)$ for certain families of sequences $c(n)$. |
| title | Asymptotics of commuting $\ell$-tuples in symmetric groups and log-concavity |
| topic | Number Theory |
| url | https://arxiv.org/abs/2401.05874 |