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.
@article{10_37236_12465,
author = {Philip D\"orr and Thomas Kahle},
title = {Extreme values of permutation statistics},
journal = {The electronic journal of combinatorics},
year = {2024},
volume = {31},
number = {3},
doi = {10.37236/12465},
zbl = {1546.60098},
url = {http://geodesic.mathdoc.fr/articles/10.37236/12465/}
}
TY - JOUR
AU - Philip Dörr
AU - Thomas Kahle
TI - Extreme values of permutation statistics
JO - The electronic journal of combinatorics
PY - 2024
VL - 31
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/12465/
DO - 10.37236/12465
ID - 10_37236_12465
ER -
%0 Journal Article
%A Philip Dörr
%A Thomas Kahle
%T Extreme values of permutation statistics
%J The electronic journal of combinatorics
%D 2024
%V 31
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/12465/
%R 10.37236/12465
%F 10_37236_12465
Philip Dörr; Thomas Kahle. Extreme values of permutation statistics. The electronic journal of combinatorics, Tome 31 (2024) no. 3. doi: 10.37236/12465
