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Pattern avoidance and Boolean elements in the Bruhat order on involutions

  • Axel Hultman
  • Kathrin Vorwerk
Article

Abstract

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

Bruhat order Boolean involutions Pattern avoidance 

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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Department of MathematicsKTHStockholmSweden

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