Pattern avoidance and the Bruhat order on involutions

Details Pattern avoidance and the Bruhat order on involutions Pattern avoidance and the Bruhat order on involutions

2007-11-14

arxiv.org/abs/0711.2223v1

Mathematics

Combinatorics

14 pages, 5 figures

Scientific paper

We show that the principal order ideal below 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.

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