Counting inversions and descents of random elements in finite Coxeter groups

DOI10.1090/mcom/3443zbMath1480.20093arXiv1802.01389OpenAlexW2786684781WikidataQ128178402 ScholiaQ128178402MaRDI QIDQ5235110

Thomas Kahle, Christian Stump

Publication date: 7 October 2019

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1802.01389

zbMATH Keywords

Coxeter groupcentral limit theoremEulerian numberspermutation statisticMahonian numbers

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Exact enumeration problems, generating functions (05A15) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Asymptotic enumeration (05A16)

Related Items (10)

Variations of central limit theorems and Stirling numbers of the first kind ⋮ A central limit theorem for descents of a Mallows permutation and its inverse ⋮ On the central limit theorem for the two-sided descent statistics in Coxeter groups ⋮ Asymptotics of a locally dependent statistic on finite reflection groups ⋮ Strange expectations and the Winnie-the-Pooh problem ⋮ Central limit theorems for generalized descents and generalized inversions in finite root systems ⋮ A natural idempotent in the descent algebra of a finite Coxeter group ⋮ On the joint distribution of descents and signs of permutations ⋮ \texttt{Findstat} -- a database and search engine for combinatorial statistics and maps ⋮ A central limit theorem for the two-sided descent statistic on Coxeter groups

Uses Software

• SageMath
• MahonianStat
• FindStat

Cites Work

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• The Mahonian probability distribution on words is asymptotically normal
• \(q\)-Eulerian polynomials arising from Coxeter groups
• Probabilistic bounds on the coefficients of polynomials with only real zeros
• Parabolic double cosets in Coxeter groups
• A central limit theorem for a new statistic on permutations
• Asymptotics of a locally dependent statistic on finite reflection groups
• Central and local limit theorems applied to asymptotic enumeration
• Mod-ϕ Convergence
• Two-Sided Eulerian Numbers via Balls in Boxes
• Unimodality, log-concavity, real-rootedness and beyond
• Combinatorics of Coxeter Groups
• Eulerian Numbers
• The 𝐬-Eulerian polynomials have only real roots
• Probability theory. A comprehensive course

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