Triangle-Free Triangulations, Hyperplane Arrangements and Shifted Tableaux
Combinatorics
2012-08-13 v2
Abstract
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.
Keywords
Cite
@article{arxiv.1009.2628,
title = {Triangle-Free Triangulations, Hyperplane Arrangements and Shifted Tableaux},
author = {Ron M. Adin and Yuval Roichman},
journal= {arXiv preprint arXiv:1009.2628},
year = {2012}
}
Comments
figure added, plus several minor changes