A Brunn-Minkowski inequality for the integer lattice

DOI10.1090/S0002-9947-01-02763-5zbMath0977.52019MaRDI QIDQ2723461

Richard J. Gardner, Paolo Gronchi

Publication date: 5 July 2001

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

zbMATH Keywords

difference setlattice polytopelattice polygonsum setlattice point enumeratorBrunn-Mikowski inequality

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) Biomedical imaging and signal processing (92C55) Polyominoes (05B50) Lattices and convex bodies in (2) dimensions (aspects of discrete geometry) (52C05)

Related Items

The Brunn-Minkowski inequality for volume differences, Reverse form of the Minkowski inequalities with applications, On Sums of Generating Sets in ℤ₂ⁿ, The Brunn-Minkowski inequality, On a Discrete Brunn--Minkowski Type Inequality, An analytic approach to cardinalities of sumsets, Brunn--Minkowski inequalities for contingency tables and integer flows, On Discrete LOG-Brunn--Minkowski Type Inequalities, Log-Brunn-Minkowski inequality under symmetry, A discrete version of Koldobsky's slicing inequality, Brunn-Minkowski type inequalities for the lattice point enumerator, Inverse additive problems for Minkowski sumsets. II, Sets in \(\mathbb{Z}^k\) with doubling \(2^k + \delta\) are near convex progressions, On Rogers–Shephard-type inequalities for the lattice point enumerator, Consequences and extensions of the Brunn-Minkowski theorem, On a characterization of lattice cubes via discrete isoperimetric inequalities, A discrete complement of Lyapunov's inequality and its information theoretic consequences, Geometric and functional inequalities for log-concave probability sequences, Triangulations and a discrete Brunn-Minkowski inequality in the plane, The Typical Approximate Structure of Sets with Bounded Sumset, Cardinality of product sets in torsion-free groups and applications in group algebras, \(L_p\) Brunn-Minkowski type inequalities for Blaschke-Minkowski homomorphisms, Inverse additive problems for Minkowski sumsets. I, On discrete Brunn-Minkowski and isoperimetric type inequalities, Brunn-Minkowski inequalities for star duals of intersection bodies and two additions, Large values of the additive energy in and, Orlicz-Brunn-Minkowski inequalities for Blaschke-Minkowski homomorphisms, Properties of two-dimensional sets with small sumset, Brunn-Minkowski and Prékopa-Leindler's inequalities under projection assumptions, A generalization of the matrix form of the Brunn-Minkowski inequality, Sums of finite subsets in \(\mathbb{R}^d\), Averaging sequences and abelian rank in amenable groups, On the discrete Brunn-Minkowski inequality by Gardner\&Gronchi, On \(p\)-quermassintegral differences function, Sums of finite subsets in \(\mathbb{R}^d\), Organic combinations of quermassintegrals and dual quermassintegrals, On the equality conditions of the Brunn-Minkowski theorem, On the classification of convex lattice polytopes, Majorization and Rényi entropy inequalities via Sperner theory, On discrete \(L_p\) Brunn-Minkowski type inequalities, On discrete Borell-Brascamp-Lieb inequalities, Entropy Inequalities for Sums in Prime Cyclic Groups, The structure of \(d\)-dimensional sets with small sumset, The polar of convex lattice sets, Bounds on the lattice point enumerator via slices and projections

Cites Work

• Capacitary inequalities of the Brunn-Minkowski type
• Compressions and isoperimetric inequalities
• Balancing extensions via Brunn-Minkowski
• On finite difference sets
• On the simplest inverse problem for sums of sets in several dimensions
• Sum of sets in several dimensions
• Sums in the grid
• A Minkowski problem for electrostatic capacity
• Shaking compact sets
• Brunn-Minkowski inequality for multiplicities
• The Set of Differences of a Given Set
• On the similarity of the entropy power inequality and the Brunn- Minkowski inequality (Corresp.)
• Information theoretic inequalities
• Discrete tomography: Determination of finite sets by X-rays
• The Structure of Homometric Sets
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item