English

A Simple Proof that Major Index and Inversions are Equidistributed

Combinatorics 2022-07-13 v1

Abstract

We present a short proof of MacMahon's classic result that the number of permutations with kk inversions equals the number whose major index (sum of positions at which descents occur) is kk

Keywords

Cite

@article{arxiv.2207.05210,
  title  = {A Simple Proof that Major Index and Inversions are Equidistributed},
  author = {Michael J. Collins},
  journal= {arXiv preprint arXiv:2207.05210},
  year   = {2022}
}
R2 v1 2026-06-25T00:49:49.830Z