Triangle-free triangulations, hyperplane arrangements and shifted tableaux
type: Item
instance of: scholarly article
title: Triangle-free triangulations, hyperplane arrangements and shifted tableaux
zbMATH Open document ID: 1253.05032
author: Yuval Roichman
author: Ron Adin
published in: The Electronic Journal of Combinatorics
publication date: 2012-10-24T00:00:00Z
full work available at URL: https://arxiv.org/abs/1009.2628
full work available at URL: v19i3p32
review text: 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}}
Mathematics Subject Classification ID: 05A19
Mathematics Subject Classification ID: 05E18
Mathematics Subject Classification ID: 05E10
Mathematics Subject Classification ID: 52C35
zbMATH DE Number: 6098374
zbMATH Keywords: Young tableaux
zbMATH Keywords: truncated shifted staircase shape
zbMATH Keywords: geodesics
describes a project that uses: AdinKingRoichman
MaRDI profile type: Publication
arXiv ID: 1009.2628
description: scientific article; zbMATH DE number 6098374