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.
@article{10_37236_2610,
author = {Ron Adin and Yuval Roichman},
title = {Triangle-free triangulations, hyperplane arrangements and shifted tableaux},
journal = {The electronic journal of combinatorics},
year = {2012},
volume = {19},
number = {3},
doi = {10.37236/2610},
zbl = {1253.05032},
url = {http://geodesic.mathdoc.fr/articles/10.37236/2610/}
}
TY - JOUR
AU - Ron Adin
AU - Yuval Roichman
TI - Triangle-free triangulations, hyperplane arrangements and shifted tableaux
JO - The electronic journal of combinatorics
PY - 2012
VL - 19
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/2610/
DO - 10.37236/2610
ID - 10_37236_2610
ER -
%0 Journal Article
%A Ron Adin
%A Yuval Roichman
%T Triangle-free triangulations, hyperplane arrangements and shifted tableaux
%J The electronic journal of combinatorics
%D 2012
%V 19
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/2610/
%R 10.37236/2610
%F 10_37236_2610
Ron Adin; Yuval Roichman. Triangle-free triangulations, hyperplane arrangements and shifted tableaux. The electronic journal of combinatorics, Tome 19 (2012) no. 3. doi: 10.37236/2610
