Corner cuts and their polytopes
type: Item
instance of: scholarly article
title: Corner cuts and their polytopes
zbMATH Open document ID: 1042.52012
author: Irene Müller
published in: Beiträge zur Algebra und Geometrie
publication date: 2003-09-02T00:00:00Z
full work available at URL: https://eudml.org/doc/230804
full work available at URL: 3.html
review text: A non-empty finite set \(\Lambda\subset\mathbb N^d\) is a corner cut if it can be separated from its complement by an affine hyperplane not containing any integral point. The corner cut polytope \(Q_n^d\) is the convex hull of the vectors \(\sum_{\lambda\in\Lambda}\lambda\) where \(\Lambda\) ranges over all corner cuts in \(\mathbb N^d\) of cardinality~\(n\). Corner cut polytopes (or staircase polytopes) have been introduced by \textit{S. Onn} and \textit{B. Sturmfels} [Adv. Appl. Math. 23, No. 1, 29--48 (1999; Zbl 0955.52008)]. The author investigates certain geometric and combinatorial properties of \(Q_n^d\) with a special focus on the planar case \(d=2\).
reviewed by: Michael Joswig
Mathematics Subject Classification ID: 52B12
zbMATH DE Number: 1973828
zbMATH Keywords: corner cut polytope
zbMATH Keywords: staircase polytope
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1973828