Restricted 3412-avoiding involutions, continued fractions, and Chebyshev polynomials

AbstractSeveral 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 generating functions for involutions which avoid 3412 and various additional patterns. We express these generating functions in terms of Chebyshev polynomials of the second kind