On the distance between the expressions of a permutation - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year : 2009

On the distance between the expressions of a permutation

Abstract

We prove that the combinatorial distance between any two reduced expressions of a given permutation of {1, ..., n} in terms of transpositions lies in O(n^4), a sharp bound. Using a connection with the intersection numbers of certain curves in van Kampen diagrams, we prove that this bound is sharp, and give a practical criterion for proving that the derivations provided by the reversing algorithm of [Dehornoy, JPAA 116 (1997) 115-197] are optimal. We also show the existence of length l expressions whose reversing requires C l^4 elementary steps.
Fichier principal
Vignette du fichier
Dhx.pdf (295.63 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-00362372 , version 1 (18-02-2009)

Identifiers

Cite

Marc Autord, Patrick Dehornoy. On the distance between the expressions of a permutation. 2009. ⟨hal-00362372⟩
50 View
76 Download

Altmetric

Share

Gmail Facebook X LinkedIn More