Corner cuts and their polytopes
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 \(d=2\).
scientific article; zbMATH DE number 1973828