Pattern avoidance and Boolean elements in the Bruhat order on involutions
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
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.
Bruhat order, Boolean involutions, Pattern avoidance, schubert varieties, coxeter groups, smoothness, intervals
IdentifiersURN: urn:nbn:se:kth:diva-18520DOI: 10.1007/s10801-008-0152-1ISI: 000267030900004ScopusID: 2-s2.0-67650355439OAI: oai:DiVA.org:kth-18520DiVA: diva2:336567
QC 201005252010-08-052010-08-052011-01-10Bibliographically approved