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.
|Number of pages||6|
|Journal||Electronic Notes in Discrete Mathematics|
|State||Published - 1 Oct 2016|
Bibliographical noteFunding 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: firstname.lastname@example.org . 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@example.com . 6 Email: firstname.lastname@example.org . 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  .
© 2016 Elsevier B.V.
- asymptotic analysis
- generating functions
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Applied Mathematics