无三角剖分、超平面排列和移位表
Triangle-Free Triangulations, Hyperplane Arrangements and Shifted Tableaux
摘要：
将凸多边形的着色无三角形三角剖分中对角线的翻转解释为在某一图形超平面排列中两个相邻腔室之间的移动。推导了相应翻转图中测地线的性质。特别是，它表明：（1）每一个对角线是翻转一次，在一个测地线之间的显着对极;（2）这些对极之间的测地线的数量等于两倍的数量的杨氏tableaux截断移位楼梯形状。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
