Autor:	Parlier, Hugo, Pournin, Lionel
Rok vydání:	2023
Předmět:	Mathematics - Geometric Topology Computer Science - Computational Geometry Mathematics - Combinatorics
Druh dokumentu:	Working Paper
Popis:	Given a surface $\Sigma$ equipped with a set $P$ of marked points, we consider the triangulations of $\Sigma$ with vertex set $P$. The flip-graph of $\Sigma$ 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 $\Sigma$ 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. Comment: 26 pages, 7 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2308.05688 Zobrazit plný text záznamu View this record from Arxiv