The distribution of descents in fixed conjugacy classes of the symmetric groups

DOI10.1006/jcta.1998.2893zbMath0917.05006OpenAlexW1981762631MaRDI QIDQ1273669

Jason Fulman

Publication date: 6 January 1999

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/2c840fd40812890fa82fb11cf4139dca2456e62a

zbMATH Keywords

generating functionsconjugacy classcycle structuremajor indexEulerian polynomialsasymptotic normality theoremdescents in permutationsdistribution of descentsnumber of descents

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Symmetric functions and generalizations (05E05) Asymptotic enumeration (05A16)

Related Items (18)

Central limit theorem for peaks of a random permutation in a fixed conjugacy class of \(S_n\) ⋮ A central limit theorem for descents of a Mallows permutation and its inverse ⋮ Martingales and descent statistics ⋮ Distribution of descents in matchings ⋮ Asymptotic normality of pattern counts in conjugacy classes ⋮ Counting permutations by peaks, descents, and cycle type ⋮ On the distribution of the major index on standard Young tableaux ⋮ Permutation statistics of products of random permutations ⋮ Plethystic formulas for permutation enumeration ⋮ A central limit theorem for descents and major indices in fixed conjugacy classes of \(S_n\) ⋮ Central limit theorem for descents in conjugacy classes of \(S_n\) ⋮ The limiting distribution of the \(q\)-derangement numbers ⋮ Asymptotic normality of the major index on standard tableaux ⋮ Card shuffling and \(P\)-partitions ⋮ Cyclic permutations: degrees and combinatorial types ⋮ On the joint distribution of descents and signs of permutations ⋮ Modifying Curtiss' theorem to prove central limit theorems ⋮ Random decompositions of Eulerian statistics

Cites Work

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• Permutation statistics and partitions
• A Mackey formula in the group of a Coxeter group. With an appendix by J. Tits: Two properties of Coxeter complexes
• Descent identities, Hessenberg varieties, and the Weil conjectures
• Counting permutations with given cycle structure and descent set
• Riffle shuffles, cycles, and descents
• Semisimple orbits of Lie algebras and card-shuffling measures on Coxeter groups
• Théorie géométrique des polynômes eulériens
• Quotients of Coxeter complexes and 𝑃-partitions
• Hessenberg Varieties

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