Extreme Values of Permutation Statistics

2022/05/03 by Philip Dörr, Dörr, Philip, Thomas Kahle +1
Computer Science · #05A16 #62R01 #Bayesian Methods and Mixture Models #Combinatorics (math.CO) #FOS: Mathematics #Primary: 60G70 #Probability (math.PR) #Secondary: 20F55

paper · pdf · doi:10.48550/arxiv.2205.01426

openalex publication_date 2022/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate extreme values of Mahonian and Eulerian distributions arising from counting inversions and descents of random elements of finite Coxeter groups. To this end, we construct a triangular array of either distribution from a sequence of Coxeter groups with increasing ranks. To avoid degeneracy of extreme values, the number of i.i.d. samples k_n in each row must be asymptotically bounded. We employ large deviations theory to prove the Gumbel attraction of Mahonian and Eulerian distributions. It is shown that for the two classes, different bounds on k_n ensure this.

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• On some Euler-Mahonian distributions
• Extremes of generalized inversions on permutation groups
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