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arXiv · 2312.08756

Asymptotic normality of pattern counts in conjugacy classes

Valentin Féray·Mohamed Slim Kammoun
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Abstract

We prove, under mild conditions on fixed points and two cycles, the asymptotic normality of vincular pattern counts for a permutation chosen uniformly at random in a conjugacy class.Additionally, we prove that the limiting variance is always non-degenerate for classical pattern counts. The proof uses weighted dependency graphs.

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Valentin Féray, Mohamed Slim Kammoun. 2024-03-11. Asymptotic normality of pattern counts in conjugacy classes. https://arxiv.org/abs/2312.08756

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