132-avoiding two-stack sortable permutations, Fibonacci numbers, and Pell numbers
نویسندگان
چکیده
منابع مشابه
132-avoiding two-stack sortable permutations, Fibonacci numbers, and Pell numbers
We describe the recursive structures of the set of two-stack sortable permutations which avoid 132 and the set of two-stack sortable permutations which contain 132 exactly once. Using these results and standard generating function techniques, we enumerate two-stack sortable permutations which avoid (or contain exactly once) 132 and which avoid (or contain exactly once) an arbitrary permutation ...
متن کاملm at h . C O / 0 20 52 06 v 1 1 9 M ay 2 00 2 132 - avoiding Two - stack Sortable Permutations , Fibonacci Numbers , and Pell Numbers ∗
In [W2] West conjectured that there are 2(3n)!/((n+1)!(2n+1)!) two-stack sortable permutations on n letters. This conjecture was proved analytically by Zeilberger in [Z]. Later, Dulucq, Gire, and Guibert [DGG] gave a combinatorial proof of this conjecture. In the present paper we study generating functions for the number of two-stack sortable permutations on n letters avoiding (or containing ex...
متن کامل1 9 M ay 2 00 2 132 - avoiding Two - stack Sortable Permutations
In [W2] West conjectured that there are 2(3n)!/((n+1)!(2n+1)!) two-stack sortable permutations on n letters. This conjecture was proved analytically by Zeilberger in [Z]. Later, Dulucq, Gire, and Guibert [DGG] gave a combinatorial proof of this conjecture. In the present paper we study generating functions for the number of two-stack sortable permutations on n letters avoiding (or containing ex...
متن کاملRestricted Permutations, Fibonacci Numbers, and k-generalized Fibonacci Numbers
In 1985 Simion and Schmidt showed that the number of permutations in Sn which avoid 132, 213, and 123 is equal to the Fibonacci number Fn+1. We use generating function and bijective techniques to give other sets of pattern-avoiding permutations which can be enumerated in terms of Fibonacci or k-generalized Fibonacci numbers.
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We investigate some arithmetic properties of the q-Fibonacci numbers and the q-Pell numbers.
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2004
ISSN: 0166-218X
DOI: 10.1016/j.dam.2003.12.007