Repetition in reduced decompositions
Combinatorics
2012-01-06 v2
Abstract
Given a permutation w, we show that the number of repeated letters in a reduced decomposition of w is always less than or equal to the number of 321- and 3412-patterns appearing in w. Moreover, we prove bijectively that the two quantities are equal if and only if w avoids the ten patterns 4321, 34512, 45123, 35412, 43512, 45132, 45213, 53412, 45312, and 45231.
Cite
@article{arxiv.1106.2839,
title = {Repetition in reduced decompositions},
author = {Bridget Eileen Tenner},
journal= {arXiv preprint arXiv:1106.2839},
year = {2012}
}
Comments
to appear in Adv. Appl. Math