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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.12513 |
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| _version_ | 1866915114300473344 |
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| author | Coopman, Michael |
| author_facet | Coopman, Michael |
| contents | For $0<q<1$, let $Maj$ be the distribution on the symmetric group $S_n$ such that a permutation $π\in S_n$ is selected with probability proportional to $q^{maj(π)}$. The distribution has connections to $q$-Plancherel measure. We describe an algorithm that realizes $Maj$, and use it to prove known results of $q$-Plancherel measure without the need of representation theory. This sampler is transparent and elegant, allowing properties of $Maj$ about its limit shape, pattern normality, and cycle structure to be obtained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_12513 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Major Index Distribution Coopman, Michael Combinatorics Probability 60C05, 05A19 For $0<q<1$, let $Maj$ be the distribution on the symmetric group $S_n$ such that a permutation $π\in S_n$ is selected with probability proportional to $q^{maj(π)}$. The distribution has connections to $q$-Plancherel measure. We describe an algorithm that realizes $Maj$, and use it to prove known results of $q$-Plancherel measure without the need of representation theory. This sampler is transparent and elegant, allowing properties of $Maj$ about its limit shape, pattern normality, and cycle structure to be obtained. |
| title | Major Index Distribution |
| topic | Combinatorics Probability 60C05, 05A19 |
| url | https://arxiv.org/abs/2501.12513 |