Pattern Avoidance and the Bruhat Order
摘要
The structure of order ideals in the Bruhat order for the symmetric group is elucidated via permutation patterns. A method for determining non-isomorphic principal order ideals is described and applied for small lengths. The permutations with boolean principal order ideals are characterized. These form an order ideal which is a simplicial poset, and its rank generating function is computed. Moreover, the permutations whose principal order ideals have a form related to boolean posets are also completely described. It is determined when the set of permutations avoiding a particular set of patterns is an order ideal, and the rank generating functions of these ideals are computed. Finally, the Bruhat order in types B and D is studied, and the elements with boolean principal order ideals are characterized and enumerated by length.
引用
@article{arxiv.math/0604322,
title = {Pattern Avoidance and the Bruhat Order},
author = {Bridget Eileen Tenner},
journal= {arXiv preprint arXiv:math/0604322},
year = {2007}
}
备注
18 pages, 7 figures