Unconditional reflexive polytopes
type: Item
instance of: scholarly article
title: Unconditional reflexive polytopes
zbMATH Open document ID: 1454.52012
author: Florian Kohl
author: McCabe Olsen
author: Raman Sanyal
published in: Discrete \& Computational Geometry
publication date: 2020-09-01T00:00:00Z
full work available at URL: https://arxiv.org/abs/1906.01469
review text: A convex polytope \(P \subset \mathbb{R}^d\) is called \textit{unconditional} if \((\sigma_1 p_1 , \dots, \sigma_d p_d) \in P\) for all \((p_1,\dots,p_d) \in P\) and all \((\sigma_1,\dots,\sigma_d)\in \{\pm 1\}^d\). The paper under review studies unconditional polytopes from the viewpoint of discrete geometry and combinatorial commutative algebra. In particular, it is shown that a lattice polytope \(P\) is an unconditional reflexive polytope if and only if \(P\) is obtained from the stable set polytope of a perfect graph. As examples, some special lattice polytopes are studied: type-B Birkhoff polytopes, signed Birkhoff polytopes, lattice polytopes arising from perfect CIS graphs, and unconditional chain polytopes of posets. Note that unconditional chain polytopes of posets were independently introduced in [\textit{H. Ohsugi} and \textit{A. Tsuchiya}, Isr. J. Math. 237, No. 1, 485--500 (2020; Zbl 1453.52013)] under the name ``enriched chain polytopes'', and the same Gröbner bases of such polytopes were constructed there.
reviewed by: Hidefumi Ohsugi
Mathematics Subject Classification ID: 52B20
Mathematics Subject Classification ID: 52B12
zbMATH DE Number: 7242486
zbMATH Keywords: perfect graphs
zbMATH Keywords: reflexive polytopes
zbMATH Keywords: unimodular triangulations
zbMATH Keywords: gale-dual pairs
zbMATH Keywords: unconditional polytopes
zbMATH Keywords: signed Birkhoff polytopes
describes a project that uses: Normaliz
describes a project that uses: OEIS
describes a project that uses: birkhoff faces
MaRDI profile type: Publication
OpenAlex ID: W3016906316
arXiv ID: 1906.01469
cites work: Hodge theory for combinatorial geometries
cites work: On graphs whose maximal cliques and stable sets intersect
cites work: Ehrhart polynomials, simplicial polytopes, magic squares and a conjecture of Stanley
cites work: Q4344117
cites work: Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties
cites work: Grid graphs, Gorenstein polytopes, and domino stackings
cites work: The Ehrhart polynomial of the Birkhoff polytope
cites work: Computing the Continuous Discretely
cites work: Combinatorial Reciprocity Theorems
cites work: Q5834711
cites work: Combinatorics of Coxeter Groups
cites work: Convex Bodies, Graphs and Partial Orders
cites work: Q5415725
cites work: Q4320807
cites work: Normality and covering properties of affine semigroups
cites work: Polytopes, Rings, and K-Theory
cites work: \(h\)-vectors of Gorenstein polytopes
cites work: The asymptotic volume of the Birkhoff polytope
cites work: Two Double Poset Polytopes
cites work: Mirror symmetry and polar duality of polytopes
cites work: Ideals, Varieties, and Algorithms
cites work: Ehrhart series of polytopes related to symmetric doubly-stochastic matrices
cites work: A generating function for all semi-magic squares and the volume of the Birkhoff polytope
cites work: Triangulations. Structures for algorithms and applications
cites work: Gorenstein algebras of Veronese type
cites work: Vertex-transitive CIS graphs
cites work: Simion's type \(B\) associahedron is a pulling triangulation of the Legendre polytope
cites work: Q3282061
cites work: Face numbers of centrally symmetric polytopes produced from Split graphs
cites work: The Martin Gardner Polytopes
cites work: Blocking and anti-blocking pairs of polyhedra
cites work: Anti-blocking polyhedra
cites work: Maximal chains and antichains
cites work: Geometric algorithms and combinatorial optimization.
cites work: Q4401003
cites work: Delannoy orthants of Legendre polytopes
cites work: Q3800169
cites work: Dual polytopes of rational convex polytopes
cites work: Classes of perfect graphs
cites work: Classification of reflexive polyhedra in three dimensions
cites work: Complete classification of reflexive polyhedra in four dimensions
cites work: Bounds for Lattice Polytopes Containing a Fixed Number of Interior Points in a Sublattice
cites work: Normal hypergraphs and the perfect graph conjecture
cites work: Kernels in perfect line-graphs
cites work: Birkhoff's theorem and convex hulls of Coxeter groups
cites work: Une caractérisation volumique de certains espaces normés de dimension finie. (A volume characterization of some finite dimensional normed spaces)
cites work: Q5817856
cites work: Gorenstein cut polytopes
cites work: Convex polytopes all of whose reverse lexicographic initial ideals are squarefree
cites work: Special simplices and Gorenstein toric rings.
cites work: Reverse lexicographic squarefree initial ideals and Gorenstein Fano polytopes
cites work: Enriched chain polytopes
cites work: Faces of Birkhoff Polytopes

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cites work: Minimal Volume-Product in Banach Spaces with a 1-Unconditional Basis

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cites work: Q3312819

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cites work: On Kalai's conjectures concerning centrally symmetric polytopes

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cites work: Convex Bodies The Brunn-MinkowskiTheory

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cites work: Q3818127

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cites work: Q4443440

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cites work: Hilbert functions of graded algebras

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cites work: Decompositions of Rational Convex Polytopes

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cites work: Two poset polytopes

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cites work: Q4294628

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cites work: A monotonicity property of \(h\)-vectors and \(h^*\)-vectors

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cites work: Q4861423

Unconditional reflexive polytopes (cites work)
cites work: Compressed polytopes and statistical disclosure limitation

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cites work: Gorenstein polytopes obtained from bipartite graphs

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cites work: Generalizations of Grillet's theorem on maximal stable sets and maximal cliques in graphs

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cites work: Lectures on Polytopes

Unconditional reflexive polytopes (DOI)
DOI: 10.1007/S00454-020-00199-8