ul 2 00 3 Restricted 3412 - Avoiding Involutions : Continued Fractions , Chebyshev Polynomials and Enumerations ∗
نویسنده
چکیده
Several authors have examined connections among restricted permutations, continued fractions, and Chebyshev polynomials of the second kind. In this paper we prove analogues of these results for involutions which avoid 3412. Our results include a recursive procedure for computing the generating function for involutions which avoid 3412 and any set of additional patterns. We use our results to give enumerations and generating functions for involutions which avoid 3412 and various sets of additional patterns. In many cases we express these generating functions in terms of Chebyshev polynomials of the second kind.
منابع مشابه
Ja n 20 04 Involutions Restricted by 3412 , Continued Fractions , and Chebyshev Polynomials
We study generating functions for the number of involutions, even involutions, and odd involutions in Sn subject to two restrictions. One restriction is that the involution avoid 3412 or contain 3412 exactly once. The other restriction is that the involution avoid another pattern τ or contain τ exactly once. In many cases we express these generating functions in terms of Chebyshev polynomials o...
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