Geodesic
Restricted Permutations and Chebyshev Polynomials
Séminaire lotharingien de combinatoire, Tome 47 (2001-2002)

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

We study generating functions for the number of permutations in Sn subject to two restrictions. One of the restrictions belongs to S3, while the other belongs to Sk. It turns out that in a large variety of cases the answer can be expressed via Chebyshev polynomials of the second kind. 

@article{SLC_2001-2002_47_a2,
     author = {Toufik Mansour and Alek Vainshtein},
     title = {Restricted {Permutations} and {Chebyshev} {Polynomials}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {47},
     year = {2001-2002},
     url = {http://geodesic.mathdoc.fr/item/SLC_2001-2002_47_a2/}
}
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Toufik Mansour; Alek Vainshtein. Restricted Permutations and Chebyshev Polynomials. Séminaire lotharingien de combinatoire, Tome 47 (2001-2002). http://geodesic.mathdoc.fr/item/SLC_2001-2002_47_a2/