Non-Leaving-Face property for marked surfaces
Combinatorics
2018-01-30 v1
Abstract
We consider the polytope arising from a marked surface by flips of triangulations. Sleator, Tarjan and Thurston studied in 1988 the diameter of the associahedron, which is the polytope arising from a marked disc by flips of triangulations. They showed that every shortest path between two vertices in a face does not leave that face. We establish that same non-leaving-face property for all unpunctured marked surfaces.
Keywords
Cite
@article{arxiv.1801.09501,
title = {Non-Leaving-Face property for marked surfaces},
author = {Thomas Brüstle and Jie Zhang},
journal= {arXiv preprint arXiv:1801.09501},
year = {2018}
}
Comments
13 pages, 12 figures