Geodesic
Restricted 132-Involutions
Séminaire lotharingien de combinatoire, Tome 48 (2002-2003) 
Olivier Guibert; Toufik Mansour. Restricted 132-Involutions. Séminaire lotharingien de combinatoire, Tome 48 (2002-2003). http://geodesic.mathdoc.fr/item/SLC_2002-2003_48_a0/
@article{SLC_2002-2003_48_a0,
     author = {Olivier Guibert and Toufik Mansour},
     title = {Restricted {132-Involutions}},
     journal = {S\'eminaire lotharingien de combinatoire},
     year = {2002-2003},
     volume = {48},
     url = {http://geodesic.mathdoc.fr/item/SLC_2002-2003_48_a0/}
}
TY  - JOUR
AU  - Olivier Guibert
AU  - Toufik Mansour
TI  - Restricted 132-Involutions
JO  - Séminaire lotharingien de combinatoire
PY  - 2002-2003
VL  - 48
UR  - http://geodesic.mathdoc.fr/item/SLC_2002-2003_48_a0/
ID  - SLC_2002-2003_48_a0
ER  - 
%0 Journal Article
%A Olivier Guibert
%A Toufik Mansour
%T Restricted 132-Involutions
%J Séminaire lotharingien de combinatoire
%D 2002-2003
%V 48
%U http://geodesic.mathdoc.fr/item/SLC_2002-2003_48_a0/
%F SLC_2002-2003_48_a0

Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website

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.