Pattern avoidance and the Bruhat order on involutions
Combinatorics
2012-07-24 v1
Abstract
We show that the principal order ideal below an element w in the Bruhat order on involutions in a symmetric group is a Boolean lattice if and only if w avoids the patterns 4321, 45312 and 456123. Similar criteria for signed permutations are also stated. Involutions with this property are enumerated with respect to natural statistics. In this context, a bijective correspondence with certain Motzkin paths is demonstrated.
Cite
@article{arxiv.0711.2223,
title = {Pattern avoidance and the Bruhat order on involutions},
author = {Axel Hultman and Kathrin Vorwerk},
journal= {arXiv preprint arXiv:0711.2223},
year = {2012}
}
Comments
14 pages, 5 figures