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

Publisher Copyright:
© 2016 Elsevier B.V.

Keywords

Triangulations
asymptotic analysis
generating functions

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

Access to Document

10.1016/j.endm.2016.09.014

Cite this

@article{878e323715214c6e91609bf15eb22687,

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 = "Publisher Copyright: {\textcopyright} 2016 Elsevier B.V.",

year = "2016",

month = oct,

day = "1",

doi = "10.1016/j.endm.2016.09.014",

language = "English",

volume = "54",

pages = "73--78",

journal = "Electronic Notes in Discrete Mathematics",

issn = "1571-0653",

publisher = "Elsevier",

}

TY - JOUR

T1 - Counting triangulations of balanced subdivisions of convex polygons

AU - Asinowski, Andrei

AU - Krattenthaler, Christain

AU - Mansour, Toufik

PY - 2016/10/1

Y1 - 2016/10/1

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.

KW - Triangulations

KW - asymptotic analysis

KW - generating functions

UR - http://www.scopus.com/inward/record.url?scp=84992626269&partnerID=8YFLogxK

U2 - 10.1016/j.endm.2016.09.014

DO - 10.1016/j.endm.2016.09.014

M3 - Article

AN - SCOPUS:84992626269

SN - 1571-0653

VL - 54

SP - 73

EP - 78

JO - Electronic Notes in Discrete Mathematics

JF - Electronic Notes in Discrete Mathematics

ER -

Counting triangulations of balanced subdivisions of convex polygons

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this