@UNPUBLISHED{publication1, title = "Diameter of a commutation class on reduced words", author = "{GUTIERRES, Gon{\c{c}}alo} and {MAMEDE, Ricardo}", year = "2023-06-01", 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.

", url = "http://www.mat.uc.pt/preprints/eng\_2023.html", note = "" }