Large chirotopes with computable numbers of triangulations
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866914384596434944 |
|---|---|
| author | Bouvel, Mathilde Féray, Valentin Goaoc, Xavier Koechlin, Florent |
| author_facet | Bouvel, Mathilde Féray, Valentin Goaoc, Xavier Koechlin, Florent |
| contents | Chirotopes are a common combinatorial abstraction of (planar) point sets. In this paper we investigate decomposition methods for chirotopes, and their application to the problem of counting the number of triangulations supported by a given planar point set. In particular, we generalize the convex and concave sums operations defined by Rutschmann and Wettstein for a particular family of chirotopes (which they call chains), and obtain a precise asymptotic estimate for the number of triangulations of the double circle, using a functional equation and the kernel method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_10251 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Large chirotopes with computable numbers of triangulations Bouvel, Mathilde Féray, Valentin Goaoc, Xavier Koechlin, Florent Computational Geometry Combinatorics Chirotopes are a common combinatorial abstraction of (planar) point sets. In this paper we investigate decomposition methods for chirotopes, and their application to the problem of counting the number of triangulations supported by a given planar point set. In particular, we generalize the convex and concave sums operations defined by Rutschmann and Wettstein for a particular family of chirotopes (which they call chains), and obtain a precise asymptotic estimate for the number of triangulations of the double circle, using a functional equation and the kernel method. |
| title | Large chirotopes with computable numbers of triangulations |
| topic | Computational Geometry Combinatorics |
| url | https://arxiv.org/abs/2603.10251 |