Depth in classical Coexter groups
Combinatorics
2017-01-13 v1
Abstract
The depth statistic was defined by Petersen and Tenner for an element of an arbitrary Coxeter group in terms of factorizations of the element into a product of reflections. It can also be defined as the minimal cost, given certain prescribed edge weights, for a path in the Bruhat graph from the identity to an element. We present algorithms for calculating the depth of an element of a classical Coxeter group that yield simple formulas for this statistic. We use our algorithms to characterize elements having depth equal to length. These are the short-braid-avoiding elements. We also give a characterization of the elements for which the reflection length coincides with both the depth and the length. These are the boolean elements.
Keywords
Cite
@article{arxiv.1507.01180,
title = {Depth in classical Coexter groups},
author = {Eli Bagno and Riccardo Biagioli and Mordechai Novick and Alexander Woo},
journal= {arXiv preprint arXiv:1507.01180},
year = {2017}
}