The expected number of inversions after n adjacent transpositions
Combinatorics
2025-09-26 v2 Probability
Abstract
We give a new expression for the expected number of inversions in the product of n random adjacent transpositions in the symmetric group S_{m+1}. We then derive from this expression the asymptotic behaviour of this number when n scales with m in various ways. Our starting point is an equivalence, due to Eriksson et al., with a problem of weighted walks confined to a triangular area of the plane.
Keywords
Cite
@article{arxiv.0909.0103,
title = {The expected number of inversions after n adjacent transpositions},
author = {Mireille Bousquet-Mélou},
journal= {arXiv preprint arXiv:0909.0103},
year = {2025}
}