English

Diagonalization of Fix-Mahonian Matrices

Combinatorics 2020-05-13 v2

Abstract

Consider the regular representation of the sum over all permutations weighted by the sum of their descent, inversion, and fixed point multinomials. We compute the spectrum and the multiplicities of its elements of that matrix. Note that those multinomial statistics allow to apply the result on several permutation statistics like the number of fixed points, of descents, of inversions, and the major index at the same time.

Keywords

Cite

@article{arxiv.2004.14417,
  title  = {Diagonalization of Fix-Mahonian Matrices},
  author = {Hery Randriamaro},
  journal= {arXiv preprint arXiv:2004.14417},
  year   = {2020}
}

Comments

16 pages

R2 v1 2026-06-23T15:11:44.655Z