Adin, Ron; Roichman, Yuval Triangle-free triangulations, hyperplane arrangements and shifted tableaux. (English) Zbl 1253.05032 Electron. J. Comb. 19, No. 3, Research Paper P32, 19 p. (2012). 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: (1)every diagonal is flipped exactly once in a geodesic between a pair of distinguished antipodes; (2) the number of geodesics between these antipodes is equal to twice the number of standard Young tableaux of a truncated shifted staircase shape. Cited in 9 Documents MSC: 05A19 Combinatorial identities, bijective combinatorics 05E18 Group actions on combinatorial structures 05E10 Combinatorial aspects of representation theory 52C35 Arrangements of points, flats, hyperplanes (aspects of discrete geometry) Keywords:Young tableaux; truncated shifted staircase shape; geodesics Software:AdinKingRoichman PDFBibTeX XMLCite \textit{R. Adin} and \textit{Y. Roichman}, Electron. J. Comb. 19, No. 3, Research Paper P32, 19 p. (2012; Zbl 1253.05032) Full Text: arXiv Link