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arXiv · 2406.12139

Fixed points of non-uniform permutations and representation theory of the symmetric group

Jason Fulman
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Abstract

We use representation theory of the symmetric group S_n to prove Poisson limit theorems for the distribution of fixed points for three types of non-uniform permutations. First, we give results for the commutator of g and x where g and x are uniform in S_n. Second, we give results for the commutator of g and x where g in uniform in S_n and x is fixed. Third, we give results for permutations obtained by multiplying n*log(n)/i + cn many random i-cycles. Some of our results are known by other, quite different, methods.

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Jason Fulman. 2024-06-27. Fixed points of non-uniform permutations and representation theory of the symmetric group. https://arxiv.org/abs/2406.12139

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