2018/01/29 by Thomas Brüstle, Jie Zhang, Brüstle, Thomas +1
Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models
paper · pdf · doi:10.48550/arxiv.1801.09501
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.