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Triangle-Free Triangulations, Hyperplane Arrangements and Shifted Tableaux

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: (1) every diagonal is flipped exactly once in a geodesic between distinguished pairs of antipodes; (2) the number of geodesics between these antipodes is equal to twice the number of Young tableaux of a truncated shifted staircase shape.

preprint2012arXivOpen access
Ron M. AdinYuval Roichman
math.CO
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Ron M. AdinYuval Roichman

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