Odd diagrams, Bruhat order, and pattern avoidance
Combinatorics
2022-02-17 v2
Abstract
The odd diagram of a permutation is a subset of the classical diagram with additional parity conditions. In this paper, we study classes of permutations with the same odd diagram, which we call odd diagram classes. First, we prove a conjecture relating odd diagram classes and 213- and 312-avoiding permutations. Secondly, we show that each odd diagram class is a Bruhat interval. Instrumental to our proofs is an explicit description of the Bruhat edges that link permutations in a class.
Cite
@article{arxiv.2009.08865,
title = {Odd diagrams, Bruhat order, and pattern avoidance},
author = {Francesco Brenti and Angela Carnevale and Bridget Eileen Tenner},
journal= {arXiv preprint arXiv:2009.08865},
year = {2022}
}
Comments
17 pages, to appear in Combinatorial Theory