The enumeration of permutations whose posets have a maximum element

Toufik Mansour

doi:10.1016/j.aam.2005.11.003

The enumeration of permutations whose posets have a maximum element

Toufik Mansour

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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 byP_{5 n} - 4 P_{5 (n - 1)} + 2 P_{5 (n - 2)} - underover(∑, j = 0, n - 2) C_j P_{5 (n - 2 - j)}, where P_n is the nth Padovan number and C_n is the nth Catalan number.

Original language	English
Pages (from-to)	434-442
Number of pages	9
Journal	Advances in Applied Mathematics
Volume	37
Issue number	4
DOIs	https://doi.org/10.1016/j.aam.2005.11.003
State	Published - Oct 2006

Keywords

Catalan numbers
Functional equations
Padovan numbers
Posets have a maximal element
Restricted permutations

ASJC Scopus subject areas

Applied Mathematics

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10.1016/j.aam.2005.11.003

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abstract = "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 byP5 n - 4 P5 (n - 1) + 2 P5 (n - 2) - underover(∑, j = 0, n - 2) Cj P5 (n - 2 - j), where Pn is the nth Padovan number and Cn is the nth Catalan number.",

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AB - 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 byP5 n - 4 P5 (n - 1) + 2 P5 (n - 2) - underover(∑, j = 0, n - 2) Cj P5 (n - 2 - j), where Pn is the nth Padovan number and Cn is the nth Catalan number.

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KW - Functional equations

KW - Padovan numbers

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KW - Restricted permutations

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The enumeration of permutations whose posets have a maximum element

Abstract

Keywords

ASJC Scopus subject areas

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