Hollow polytopes of large width

DOI10.1090/proc/14721zbMath1445.52012arXiv1812.00916OpenAlexW2950273625MaRDI QIDQ5210954

Giulia Codenotti, Francisco Santos

Publication date: 16 January 2020

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1812.00916

zbMATH Keywords

lattice polytopeflatness theoremlattice widthlattice-freehollow convex body

Mathematics Subject Classification ID

Lattices and convex bodies in (n) dimensions (aspects of discrete geometry) (52C07) Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) (52B20) Packing and covering in (n) dimensions (aspects of discrete geometry) (52C17)

Related Items

Lattice-free simplices with lattice width \(2d - o(d)\), Enumeration and unimodular equivalence of empty delta-modular simplices, Generalized flatness constants, spanning lattice polytopes, and the Gromov width, Normal polytopes and ellipsoids, A local maximizer for lattice width of 3-dimensional hollow bodies, The complete classification of empty lattice 4-simplices, A generalization of a theorem of White

Cites Work

• Maximal lattice-free polyhedra: finiteness and an explicit description in dimension three
• Inequalities for the lattice width of lattice-free convex sets in the plane
• Lifting properties of maximal lattice-free polyhedra
• Blowing up convex sets in the plane
• Covering minima and lattice-point-free convex bodies
• Inequalities for convex bodies and polar reciprocal lattices in \(\mathbb{R}^ n\). II: Application of \(K\)-convexity
• On the maximal width of empty lattice simplices
• Distances between non-symmetric convex bodies and the \(MM^*\)-estimate
• Lattice-free sets, multi-branch split disjunctions, and mixed-integer programming
• Notions of Maximality for Integral Lattice-Free Polyhedra: The Case of Dimension Three
• Classification of empty lattice 4-simplices of width larger than two
• The Flatness Theorem for Nonsymmetric Convex Bodies via the Local Theory of Banach Spaces
• Lattice Tetrahedra
• Unnamed Item
• Unnamed Item
• Unnamed Item