Groupoid cardinality and random permutations

If we treat the symmetric group S_n as a probability measure space where each element has measure 1/n!, then the number of cycles in a permutation becomes a random variable. The Cycle Length Lemma describes the expected values of products of these random variables. Here we categorify the Cycle Lengt...

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Bibliographic Details
Published inTheory and applications of categories Vol. 44; no. 14; pp. 410 - 419
Main Author Baez, John C.
Format Journal Article
LanguageEnglish
Published Sackville R. Rosebrugh 2025
Subjects
Finite element analysis
Permutations
Probability
Probability distribution
Proof theory
Random variables
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ISSN1201-561X
1201-561X
DOI10.70930/tac/94l2qrji

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Summary:If we treat the symmetric group S_n as a probability measure space where each element has measure 1/n!, then the number of cycles in a permutation becomes a random variable. The Cycle Length Lemma describes the expected values of products of these random variables. Here we categorify the Cycle Length Lemma by showing that it follows from an equivalence between groupoids.
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content type line 14
ISSN:1201-561X
1201-561X
DOI:10.70930/tac/94l2qrji