Diameter of the commutation classes graph of a permutation
Combinatorics
2022-03-09 v2
Abstract
We define a statistic on the graph of commutation classes of a permutation of the symmetric group which is used to show that these graphs are equipped with a ranked poset structure, with a minimum and maximum. This characterization also allows us to compute the diameter of the commutation graph for any permutation, from which the results for the longest permutation and for fully commutative permutations are recovered.
Cite
@article{arxiv.2202.07313,
title = {Diameter of the commutation classes graph of a permutation},
author = {G. Gutierres and R. Mamede and J. L. Santos},
journal= {arXiv preprint arXiv:2202.07313},
year = {2022}
}
Comments
Some typos corrected and references added