Counting triangulations of balanced subdivisions of convex polygons

Andrei Asinowski, Christain Krattenthaler, Toufik Mansour

Research output: Contribution to journalArticlepeer-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 languageEnglish
Pages (from-to)73-78
Number of pages6
JournalElectronic Notes in Discrete Mathematics
Volume54
DOIs
StatePublished - 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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