Restricted 132 - Involutions
نویسنده
چکیده
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 τ 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.
منابع مشابه
ar X iv : m at h / 02 06 16 9 v 1 [ m at h . C O ] 1 7 Ju n 20 02 SOME STATISTICS ON RESTRICTED 132 INVOLUTIONS
In [GM] Guibert and Mansour studied involutions on n letters avoiding (or containing exactly once) 132 and avoiding (or containing exactly once) an arbitrary pattern on k letters. They also established a bijection between 132-avoiding involutions and Dyck word prefixes of same length. Extending this bijection to bilateral words allows to determine more parameters; in particular, we consider the...
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