Pattern avoidance and Boolean elements in the Bruhat order on involutions
Journal of Algebraic Combinatorics, Tome 30 (2009) no. 1, pp. 87-102.

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Summary: 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.
Keywords: keywords Bruhat order, Boolean involutions, pattern avoidance
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Hultman, Axel; Vorwerk, Kathrin. Pattern avoidance and Boolean elements in the Bruhat order on involutions. Journal of Algebraic Combinatorics, Tome 30 (2009) no. 1, pp. 87-102. http://geodesic.mathdoc.fr/item/JAC_2009__30_1_a2/