FB 6 Mathematik/Informatik

Institut für Mathematik

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SS 2019

10.04.2019 um 17:15 Uhr in 69/125

Prof. Dr. Christian Stump (Ruhr-Universität Bochum)

Counting Inversions and Descents of Random Elements in Finite Coxeter Groups 

"Permutation statistics" (this is, assigning numbers to permutations) is a fundamental concept from Combinatorics. Among the most important are the Mahonian and Eulerian numbers given by the number of inversions and by the number of descents. in this talk I report on Mahonian and Eulerian statistics in general finite Coxeter groups by discussing properties of their probability distributions that we exhibited using the Combinatorial Statistics Database FindStat. I will provide uniform formulas for their mean values and variances in terms of Coxeter group data, and I will also discuss the double-Eulerian probability distribution given by the sum of descents and inverse descents. I will finally establish necessary and sufficient conditions for general sequences of finite Coxeter groups of increasing rank for which Mahonian and Eulerian probability distributions satisfy central and local limit theorems. This talk is based on recent collaborations with Thomas Kahle.