Restricted 132-alternating Permutations and Chebyshev Polynomials
نویسنده
چکیده
A permutation is said to be alternating if it starts with rise and then descents and rises come in turn. In this paper we study the generating function for the number of alternating permutations on n letters that avoid or contain exactly once 132 and also avoid or contain exactly once an arbitrary pattern on k letters. In several interesting cases the generating function depends only on k and is expressed via Chebyshev polynomials of the second kind.
منابع مشابه
Horse paths, restricted 132-avoiding permutations, continued fractions, and Chebyshev polynomials
Several authors have examined connections among 132-avoiding permutations, continued fractions, and Chebyshev polynomials of the second kind. In this paper we find analogues for some of these results for permutations π avoiding 132 and 1223 (there is no occurrence πi < πj < πj+1 such that 1 ≤ i ≤ j − 2) and provide a combinatorial interpretation for such permutations in terms of lattice paths. ...
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