Counting triangulations of balanced subdivisions of convex polygons

Andrei Asinowski; Christain Krattenthaler; Toufik Mansour

doi:10.1016/j.endm.2016.09.014

Counting triangulations of balanced subdivisions of convex polygons

Andrei Asinowski, Christain Krattenthaler, Toufik Mansour

Department of Mathematics

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

Abstract

We compute the number of triangulations of a convex k-gon each of whose sides is subdivided by r−1 points. We find explicit formulas and generating functions, and we determine the asymptotic behaviour of these numbers as k and/or r tend to infinity. We connect these results with the question of finding the planar set of n points in general position that has the minimum possible number of triangulations.

Original language	English
Pages (from-to)	73-78
Number of pages	6
Journal	Electronic Notes in Discrete Mathematics
Volume	54
DOIs	https://doi.org/10.1016/j.endm.2016.09.014
State	Published - 1 Oct 2016

Bibliographical note

Funding Information:
1 See http://arxiv.org/abs/1604.02870 for a preprint of the full version of this paper. 2 Research supported by the Austrian Science Foundation FWF, grant S50-N15, in the framework of the Special Research Program “Algorithmic and Enumerative Combinatorics”. 3 Email: andrei.asinowski@tuwien.ac.at . 4 Research partially supported by the Austrian Science Foundation FWF, grant S50-N15, in the framework of the Special Research Program “Algorithmic and Enumerative Combinatorics”. 5 Email: christian.krattenthaler@univie.ac.at . 6 Email: toufik@math.haifa.ac.il . 7 Notice the difference in notation: our k is their r, and our r is their k + 1. 8 An equivalent formula was found in the earlier work [4] [2].

Publisher Copyright:
© 2016 Elsevier B.V.

Keywords

Triangulations
asymptotic analysis
generating functions

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

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10.1016/j.endm.2016.09.014

Cite this

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title = "Counting triangulations of balanced subdivisions of convex polygons",

abstract = "We compute the number of triangulations of a convex k-gon each of whose sides is subdivided by r−1 points. We find explicit formulas and generating functions, and we determine the asymptotic behaviour of these numbers as k and/or r tend to infinity. We connect these results with the question of finding the planar set of n points in general position that has the minimum possible number of triangulations.",

keywords = "Triangulations, asymptotic analysis, generating functions",

author = "Andrei Asinowski and Christain Krattenthaler and Toufik Mansour",

note = "Funding Information: 1 See http://arxiv.org/abs/1604.02870 for a preprint of the full version of this paper. 2 Research supported by the Austrian Science Foundation FWF, grant S50-N15, in the framework of the Special Research Program “Algorithmic and Enumerative Combinatorics”. 3 Email: andrei.asinowski@tuwien.ac.at . 4 Research partially supported by the Austrian Science Foundation FWF, grant S50-N15, in the framework of the Special Research Program “Algorithmic and Enumerative Combinatorics”. 5 Email: christian.krattenthaler@univie.ac.at . 6 Email: toufik@math.haifa.ac.il . 7 Notice the difference in notation: our k is their r, and our r is their k + 1. 8 An equivalent formula was found in the earlier work [4] [2]. Publisher Copyright: {\textcopyright} 2016 Elsevier B.V.",

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AU - Krattenthaler, Christain

AU - Mansour, Toufik

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N2 - We compute the number of triangulations of a convex k-gon each of whose sides is subdivided by r−1 points. We find explicit formulas and generating functions, and we determine the asymptotic behaviour of these numbers as k and/or r tend to infinity. We connect these results with the question of finding the planar set of n points in general position that has the minimum possible number of triangulations.

AB - We compute the number of triangulations of a convex k-gon each of whose sides is subdivided by r−1 points. We find explicit formulas and generating functions, and we determine the asymptotic behaviour of these numbers as k and/or r tend to infinity. We connect these results with the question of finding the planar set of n points in general position that has the minimum possible number of triangulations.

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KW - asymptotic analysis

KW - generating functions

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ER -

Counting triangulations of balanced subdivisions of convex polygons

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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