The enumeration of permutations whose posets have a maximum element

被引：1
作者：
Mansour, Toufik [1 ]
机构：
[1] Univ Haifa, Dept Math, IL-31905 Haifa, Israel
[2] Nankai Univ, Ctr Combinator, LPMC, Tianjin 300071, Peoples R China
来源：
ADVANCES IN APPLIED MATHEMATICS | 2006年 / 37卷 / 04期
关键词：
Catalan numbers; functional equations; Padovan numbers; posets have a maximal element; restricted permutations;
D O I：
10.1016/j.aam.2005.11.003
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Recently, Tenner [B.E. Tenner, Reduced decompositions and permutation patterns, J. Algebraic. Combin., in press, preprint arXiv: math. CO/0506242] studied the set of posets of a permutation of length n with unique maximal element, which arise naturally when studying the set of zonotopal tilings of Elnitsky's polygon. In this paper, we prove that the number of such posets is given by P-5n - 4P(5(n-1))+2P(5(n-2)) - Sigma(n-2)(j=0) C-j P5(n-2-j), where P-n is the nth Padovan number and C-n is the nth Catalan number. (C) 2006 Elsevier Inc. All rights reserved.
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页码：434 / 442
页数：9
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