Pattern avoidance and the Bruhat order

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:114

Article

Tenner, Bridget Eileen

关键词: Bruhat order;    coxeter group;    pattern;    reduced decomposition;    order ideal;    interval;    boolean poser;   

DOI  :  10.1016/j.jcta.2006.10.003

来源: Elsevier

【 摘 要 】

The structure of order ideals in the Bruhat order for the symmetric group is elucidated via permutation patterns. The permutations with boolean principal order ideals are characterized. These form an order ideal which is a simplicial poser, 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. (c) 2006 Elsevier Inc. All rights reserved.

【 授权许可】

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