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Pattern avoidance and Boolean elements in the Bruhat order on involutions
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2009 (English)In: Journal of Algebraic Combinatorics, ISSN 0925-9899, E-ISSN 1572-9192, Vol. 30, no 1, 87-102 p.Article in journal (Refereed) Published
Abstract [en]

We show that the principal order ideal of 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.

Place, publisher, year, edition, pages
2009. Vol. 30, no 1, 87-102 p.
Keyword [en]
Bruhat order, Boolean involutions, Pattern avoidance, schubert varieties, coxeter groups, smoothness, intervals
Identifiers
URN: urn:nbn:se:kth:diva-18520DOI: 10.1007/s10801-008-0152-1ISI: 000267030900004Scopus ID: 2-s2.0-67650355439OAI: oai:DiVA.org:kth-18520DiVA: diva2:336567
Note
QC 20100525Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2017-12-12Bibliographically approved

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