English

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

R2 v1 2026-06-23T00:01:07.035Z