Triangle-Free Triangulations, Hyperplane Arrangements and Shifted Tableaux

Details Triangle-Free Triangulations, Hyperplane Arrangements and Shifted Tableaux Triangle-Free Triangulations, Hyperplane Arrangements and Shifted Tableaux

2010-09-14

arxiv.org/abs/1009.2628v1

Mathematics

Combinatorics

16 pages, 1 figure

Scientific paper

Flips of diagonals in colored triangle-free triangulations of a convex polygon are interpreted as moves between two adjacent chambers in a certain graphic hyperplane arrangement. Properties of geodesics in the associated flip graph are deduced. In particular, it is shown that every diagonal is flipped exactly once in a geodesic between distinguished pairs of antipodes, and that the number of geodesics between distinguished antipodes is equal to twice the number of Young tableaux of a truncated shifted staircase shape.

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