On the distance between the expressions of a permutation
Combinatorics
2009-02-19 v1
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.
Keywords
Cite
@article{arxiv.0902.3074,
title = {On the distance between the expressions of a permutation},
author = {Marc Autord and Patrick Dehornoy},
journal= {arXiv preprint arXiv:0902.3074},
year = {2009}
}