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Boolean elements in the Bruhat order on twisted involutions

2012
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Involve. A Journal of Mathematics
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We prove that a permutation in the Bruhat order on twisted involutions is Boolean if and only if it avoids the following patterns: 4321, 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. We first define some requisite terms in the problem statement (see [Björner and Brenti 2005] for background reading). Definition. Let denote the number of inversions of w. The

doi:10.2140/involve.2012.5.339
fatcat:p2dqw7nd2jbohc6jy74d6rpdsq