Pattern expansions of permutation statistics
Combinatorics
2026-01-08 v1
Abstract
We study the expansions of permutation statistics in the basis of functions counting occurrences of a fixed pattern in a permutation. We show the finiteness of these pattern expansions for a class of permutation statistics including the higher moment statistics, generalizing a result of Berman and Tenner. We also give a combinatorial criterion for the positivity of pattern expansions. Using this criterion, we show that the pattern expansion of the number of reduced words of a permutation is positive and give an enumerative interpretation for the coefficients.
Cite
@article{arxiv.2601.03918,
title = {Pattern expansions of permutation statistics},
author = {Ian Cavey and Hugh Dennin and Bridget Eileen Tenner},
journal= {arXiv preprint arXiv:2601.03918},
year = {2026}
}
Comments
21 pages