9 M ay 2 00 1 COUNTING OCCURENCES OF 132 IN A PERMUTATION
نویسندگان
چکیده
We study the generating function for the number of permutations on n letters containing exactly r > 0 occurences of 132. It is shown that finding this function for a given r amounts to a routine check of all permutations in S2r . 2000 Mathematics Subject Classification: Primary 05A05, 05A15; Secondary 05C90
منابع مشابه
m 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 کامل1 9 M ay 2 00 2 132 - avoiding Two - stack
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 کاملar X iv : m at h / 01 05 07 3 v 2 [ m at h . C O ] 2 A ug 2 00 1 COUNTING OCCURRENCES OF 132 IN A PERMUTATION
We study the generating function for the number of permutations on n letters containing exactly r > 0 occurrences of 132. It is shown that finding this function for a given r amounts to a routine check of all permutations in S2r . 2000 Mathematics Subject Classification: Primary 05A05, 05A15; Secondary 05C90
متن کاملN ov 2 00 6 Permutations Avoiding a Nonconsecutive Instance of a 2 - or 3 - Letter Pattern
We count permutations avoiding a nonconsecutive instance of a two-or three-letter pattern, that is, the pattern may occur but only as consecutive entries in the permutation. Two-letter patterns give rise to the Fibonacci numbers. The counting sequences for the two representative three-letter patterns, 321 and 132, have respective generating functions (1 + x 2)(C(x) − 1)/(1 + x + x 2 − xC(x)) an...
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تاریخ انتشار 2001