## 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.

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 |
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State | Published - 2016 |

Event | 10th edition of the Jornadas de Matematica Discreta y Algoritmica, JMDA2016 - Duration: 1 Jan 2016 → … |

### Conference

Conference | 10th edition of the Jornadas de Matematica Discreta y Algoritmica, JMDA2016 |
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Period | 1/01/16 → … |

### 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