Counting geodesics between surface triangulations
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916655561441280 |
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| author | Parlier, Hugo Pournin, Lionel |
| author_facet | Parlier, Hugo Pournin, Lionel |
| contents | Given a surface $Σ$ equipped with a set $P$ of marked points, we consider the triangulations of $Σ$ with vertex set $P$. The flip-graph of $Σ$ whose vertices are these triangulations, and whose edges correspond to flipping arcs appears in the study of moduli spaces and mapping class groups. We consider the number of geodesics in the flip-graph of $Σ$ between two triangulations as a function of their distance. We show that this number grows exponentially provided the surface has enough topology, and that in the remaining cases the growth is polynomial. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_05688 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Counting geodesics between surface triangulations Parlier, Hugo Pournin, Lionel Geometric Topology Computational Geometry Combinatorics Given a surface $Σ$ equipped with a set $P$ of marked points, we consider the triangulations of $Σ$ with vertex set $P$. The flip-graph of $Σ$ whose vertices are these triangulations, and whose edges correspond to flipping arcs appears in the study of moduli spaces and mapping class groups. We consider the number of geodesics in the flip-graph of $Σ$ between two triangulations as a function of their distance. We show that this number grows exponentially provided the surface has enough topology, and that in the remaining cases the growth is polynomial. |
| title | Counting geodesics between surface triangulations |
| topic | Geometric Topology Computational Geometry Combinatorics |
| url | https://arxiv.org/abs/2308.05688 |