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 |
|---|---|
| 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 |
|---|---|
| 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: [email protected] . 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: [email protected] . 6 Email: [email protected] . 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