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Séminaire Lotharingien de Combinatoire, B48a (2002), 23 pp.

# Olivier Guibert and Toufik Mansour

#
Restricted 132-Involutions

**Abstract.**
We study generating functions for the number of involutions of length *n*
avoiding (or containing exactly once) 132 and avoiding
(or containing exactly once) an arbitrary permutation *\tau*
of length *k*. In several interesting cases these generating functions
depend only on *k* and can be expressed via Chebyshev polynomials of
the second kind. In particular, we show that involutions of length *n*
avoiding both 132 and 12...k are equinumerous with involutions
of length *n* avoiding both 132 and any *extended double-wedge
pattern* of length *k*.
We use combinatorial methods to prove several of our results.

Received: January 16, 2002;
Revised: April 30, 2002; July 14, 2002;
Accepted: August 7, 2002.

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