Frontiers of Mathematics in China >

2019 , Vol. 14 >Issue 3: 521 - 534

DOI: https://doi.org/10.1007/s11464-019-0767-7

RESEARCH ARTICLE

Non-leaving-face property for marked surfaces

  • Thomas BRÜSTLE 1 ,
  • Jie ZHANG , 2
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  • 1. Département de Mathématiques, Université de Sherbrooke, Sherbrooke, J1K 2R1, Canada
  • 2. School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China

Received date: 12 Jul 2018

Accepted date: 09 Apr 2019

Published date: 15 Jun 2019

Copyright

2019 Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature
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Abstract

We consider the polytope arising from a marked surface by flips of triangulations. D. D. Sleator, R. E. Tarjan, and W. P. Thurston [J. Amer. Math. Soc., 1988, 1(3): 647{681] studied 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 give a new method, which is different from the one used by V. Disarlo and H. Parlier [arXiv: 1411.4285] to establish the same non-leaving-face property for all unpunctured marked surfaces.

Key words： Marked surface; non-leaving-face property; exchange graph

Cite this article

Thomas BRÜSTLE , Jie ZHANG . Non-leaving-face property for marked surfaces[J]. Frontiers of Mathematics in China, 2019 , 14(3) : 521 -534 . DOI: 10.1007/s11464-019-0767-7

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