<Reference List> | |
Type: | Preprint |
National /International: | International |
Title: | Diameter of a commutation class on reduced words |
Publication Date: | 2023-06-01 |
Authors: |
- Gonçalo Gutierres
- Ricardo Mamede |
Abstract: | Any permutation w of the symmetric group can be generated by a product of adjacent transpositions, and a reduced word for w is a sequence of generators of minimal length whose product is w. The main result in this paper gives a formula to compute the diameter of a commutation class of the graph G(w), whose vertices are reduced words for w and whose edges are braid relations. To do so, we define a metric on the set of all reduced words of a given permutation which turn out to be equal to the usual distance in any commutation class. If a permutation is fully commutative, i.e. it has only one commutation class, then the formula gives the diameter of G(w). The diameter for a Grassmanian permutation is also given in terms of its Lehman code. |
Institution: | DMUC 23-17 |
Online version: | http://www.mat.uc.pt...prints/eng_2023.html |
Download: | Not available |