Vol. 5, No. 3, 2012

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ISSN: 1944-4184 (e-only)
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Boolean elements in the Bruhat order on twisted involutions

Delong Meng

Vol. 5 (2012), No. 3, 339–348
Abstract

We prove that a permutation in the Bruhat order on twisted involutions is Boolean if and only if it avoids the following patterns: 4321, 3421, 4312, 4231, 32541, 52143, 351624, 456123, 426153, 321654, 561234, 345612, 3416275, 3561274, 1532746, 4517236, 34127856, 35172846, and 36712845. This result answers a question proposed by Hultman and Vorwerk. Our technique provides an application of the pictorial representation of the Bruhat order given by Incitti.

Keywords
pattern avoidance, Bruhat order, twisted involutions, Boolean posets
Mathematical Subject Classification 2010
Primary: 05E15
Milestones
Received: 17 September 2011
Accepted: 22 September 2011
Published: 14 April 2013

Communicated by Kenneth S. Berenhaut
Authors
Delong Meng
Department of Mathematics
Massachusetts Institute of Technology
77 Massachusetts Avenue
Cambridge, MA 02139
United States