Triangle-free triangulations, hyperplane arrangements and shifted tableaux
Summary: 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: {\parindent=7mm \begin{itemize}\item[(1)]every diagonal is flipped exactly once in a geodesic between a pair of distinguished antipodes; \item[(2)] the number of geodesics between these antipodes is equal to twice the number of standard Young tableaux of a truncated shifted staircase shape. \end{itemize}}
scientific article; zbMATH DE number 6098374