Reduced decompositions and commutation classes
Combinatorics
2010-09-07 v1
Abstract
We study three aspects of commutation classes of reduced decompositions: the number of commutation classes, the structures of their corresponding graphs, and the enumeration of subnetworks, a concept recently introduced by Warrington [21]. Our bound for the number of commutation classes generalizes the works of Knuth[12], Green and Losonczy [7], and Tenner [19]. We analyze the structure of the graph G(w) using pattern avoidance, which provides an application of Tenner's characterization of vexillary permutations in [19]. We also discuss some connections between our work and recent developments in the strong Bruhat order and the higher Bruhat order.
Cite
@article{arxiv.1009.0886,
title = {Reduced decompositions and commutation classes},
author = {Delong Meng},
journal= {arXiv preprint arXiv:1009.0886},
year = {2010}
}