Grid polygons from permutations and their enumeration by the kernel method

Toufik Mansour; Simone Severini

Grid polygons from permutations and their enumeration by the kernel method

Department of Mathematics

Research output: Contribution to conference › Paper › peer-review

Abstract

A grid polygon is a polygon whose vertices are points of a grid. We define an injective map between permutations of length n and a subset of grid polygons on n vertices, which we call consecutive-minima polygons. By the kernel method, we enumerate sets of permutations whose consecutive-minima polygons satisfy specific geometric conditions. We deal with 2-variate and 3-variate generating functions.

Original language	English
State	Published - 2007
Event	19th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'07 - Tianjin, China Duration: 2 Jul 2007 → 6 Jul 2007

Conference

Conference	19th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'07
Country/Territory	China
City	Tianjin
Period	2/07/07 → 6/07/07

Keywords

Grid polygons
Kernel method
Permutations

ASJC Scopus subject areas

Algebra and Number Theory

Cite this

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title = "Grid polygons from permutations and their enumeration by the kernel method",

abstract = "A grid polygon is a polygon whose vertices are points of a grid. We define an injective map between permutations of length n and a subset of grid polygons on n vertices, which we call consecutive-minima polygons. By the kernel method, we enumerate sets of permutations whose consecutive-minima polygons satisfy specific geometric conditions. We deal with 2-variate and 3-variate generating functions.",

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author = "Toufik Mansour and Simone Severini",

year = "2007",

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note = "19th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'07 ; Conference date: 02-07-2007 Through 06-07-2007",

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T1 - Grid polygons from permutations and their enumeration by the kernel method

AU - Mansour, Toufik

AU - Severini, Simone

PY - 2007

Y1 - 2007

N2 - A grid polygon is a polygon whose vertices are points of a grid. We define an injective map between permutations of length n and a subset of grid polygons on n vertices, which we call consecutive-minima polygons. By the kernel method, we enumerate sets of permutations whose consecutive-minima polygons satisfy specific geometric conditions. We deal with 2-variate and 3-variate generating functions.

AB - A grid polygon is a polygon whose vertices are points of a grid. We define an injective map between permutations of length n and a subset of grid polygons on n vertices, which we call consecutive-minima polygons. By the kernel method, we enumerate sets of permutations whose consecutive-minima polygons satisfy specific geometric conditions. We deal with 2-variate and 3-variate generating functions.

KW - Grid polygons

KW - Kernel method

KW - Permutations

UR - http://www.scopus.com/inward/record.url?scp=84860749872&partnerID=8YFLogxK

M3 - Paper

AN - SCOPUS:84860749872

T2 - 19th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'07

Y2 - 2 July 2007 through 6 July 2007

ER -

Grid polygons from permutations and their enumeration by the kernel method

Abstract

Conference

Keywords

ASJC Scopus subject areas

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Cite this