European Journal of Combinatorics, ISSN 0195-6698, 06/2019, Volume 79, pp. 27 - 45

For a -dimensional polytope with vertices, , we calculate precisely the minimum possible number of -dimensional faces, when or . This confirms a conjecture of...

Mathematics - Combinatorics

Mathematics - Combinatorics

Journal Article

Discrete & Computational Geometry, ISSN 0179-5376, 9/2018, Volume 60, Issue 2, pp. 512 - 529

This paper concerns the facial geometry of the set of $$n \times n$$ n×n correlation matrices. The main result states that almost every set of r vertices...

Cut polytope | Computational Mathematics and Numerical Analysis | Elliptope | Matrix concentration | Correlation matrix | Probabilistic method | 15B48 | Mathematics | 90C27 | Secondary: 52B12 | Combinatorics | Face | Primary: 52A20 | MATHEMATICS | OPTIMIZATION | COMPUTER SCIENCE, THEORY & METHODS | MAX-CUT PROBLEM | Correlation

Cut polytope | Computational Mathematics and Numerical Analysis | Elliptope | Matrix concentration | Correlation matrix | Probabilistic method | 15B48 | Mathematics | 90C27 | Secondary: 52B12 | Combinatorics | Face | Primary: 52A20 | MATHEMATICS | OPTIMIZATION | COMPUTER SCIENCE, THEORY & METHODS | MAX-CUT PROBLEM | Correlation

Journal Article

Mathematics of Operations Research, ISSN 0364-765X, 11/2019

Journal Article

Forum Mathematicum, ISSN 0933-7741, 11/2017, Volume 29, Issue 6, pp. 1371 - 1411

There are two interesting families of -operads, those that detect double loop spaces, and those that solve Deligne’s conjecture on Hochschild cochains. The...

55P48 | Permutohedra | 52B12 | 55P35 | configuration spaces | little discs | 55R80

55P48 | Permutohedra | 52B12 | 55P35 | configuration spaces | little discs | 55R80

Journal Article

Bulletin of the London Mathematical Society, ISSN 0024-6093, 06/2019, Volume 51, Issue 3, pp. 406 - 420

For any lattice congruence of the weak order on Sn, N. Reading proved that glueing together the cones of the braid fan that belong to the same congruence class...

06B10 (primary) | 52B12 | 52B11 | 03G10 | Combinatorics | Metric Geometry | Mathematics

06B10 (primary) | 52B12 | 52B11 | 03G10 | Combinatorics | Metric Geometry | Mathematics

Journal Article

The American Mathematical Monthly, ISSN 0002-9890, 10/2018, Volume 125, Issue 9, pp. 820 - 828

The Mahler volume is, intuitively speaking, a measure of how "round" a centrally symmetric convex body is. In one direction, this intuition is given weight by...

MSC: Primary 52B12 | MATHEMATICS

MSC: Primary 52B12 | MATHEMATICS

Journal Article

Discrete & Computational Geometry, ISSN 0179-5376, 3/2019, Volume 61, Issue 2, pp. 285 - 302

Blind and Mani, and later Kalai, showed that the face lattice of a simple polytope is determined by its graph, namely its 1-skeleton. Call a vertex of a...

Reconstruction | Computational Mathematics and Numerical Analysis | Secondary 52B12 | k -Skeleton | Simple polytope | Mathematics | Combinatorics | Primary 52B05 | k-Skeleton | MATHEMATICS | COMPUTER SCIENCE, THEORY & METHODS | Polytopes | Lattices | Graph theory

Reconstruction | Computational Mathematics and Numerical Analysis | Secondary 52B12 | k -Skeleton | Simple polytope | Mathematics | Combinatorics | Primary 52B05 | k-Skeleton | MATHEMATICS | COMPUTER SCIENCE, THEORY & METHODS | Polytopes | Lattices | Graph theory

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 05/2015, Volume 143, Issue 5, pp. 1891 - 1895

We study the tropicalization of the cone of positive semidefinite matrices over the ordered field of real Puiseux series. The tropical PSD matrices form the...

MATHEMATICS | MATHEMATICS, APPLIED | Mathematics - Combinatorics

MATHEMATICS | MATHEMATICS, APPLIED | Mathematics - Combinatorics

Journal Article

Boletín de la Sociedad Matemática Mexicana, ISSN 1405-213X, 4/2015, Volume 21, Issue 1, pp. 39 - 51

We show that there are exactly 126 combinatorially distinct simplicial, neighbourly 5-polytopes with nine vertices, and give their constructions.

52B05 | Mathematics, general | Mathematics | 52C35 | 52B12 | 52B11

52B05 | Mathematics, general | Mathematics | 52C35 | 52B12 | 52B11

Journal Article

Experimental Mathematics, ISSN 1058-6458, 10/2018, Volume 27, Issue 4, pp. 377 - 394

A k-associahedron is a simplicial complex whose facets, called k-triangulations, are the inclusion maximal sets of diagonals of a convex polygon where no k + 1...

multiassociahedra | 52B40 | 52B12 | 52B11 | subword complexes | multitriangulations | 05E45 | fans | MATHEMATICS | TRIANGULATIONS | Mathematics - Combinatorics

multiassociahedra | 52B40 | 52B12 | 52B11 | subword complexes | multitriangulations | 05E45 | fans | MATHEMATICS | TRIANGULATIONS | Mathematics - Combinatorics

Journal Article

Discrete & Computational Geometry, ISSN 0179-5376, 4/2019, Volume 61, Issue 3, pp. 653 - 660

A Euclidean distance matrix $$D(\alpha )$$ D ( α ) is defined by $$D_{ij}=(\alpha _i-\alpha _j)^2$$ D ij = ( α i - α j ) 2 , where $$\alpha =(\alpha _1,\ldots...

Computational Mathematics and Numerical Analysis | Positive semidefinite rank | 52B12 | 81P45 | Nonnegative matrix factorization | 15A23 | Mathematics | Communication complexity | Combinatorics | Extended formulations of polytopes | MATHEMATICS | LOWER BOUNDS | POLYTOPES | COMPUTER SCIENCE, THEORY & METHODS | Computer network protocols | Euclidean geometry | Complexity theory

Computational Mathematics and Numerical Analysis | Positive semidefinite rank | 52B12 | 81P45 | Nonnegative matrix factorization | 15A23 | Mathematics | Communication complexity | Combinatorics | Extended formulations of polytopes | MATHEMATICS | LOWER BOUNDS | POLYTOPES | COMPUTER SCIENCE, THEORY & METHODS | Computer network protocols | Euclidean geometry | Complexity theory

Journal Article

Experimental Mathematics, ISSN 1058-6458, 01/2019, Volume 28, Issue 1, pp. 115 - 120

In this short note, we give large counterexamples to natural questions about certain order polytopes, in particular, Gelfand-Tsetlin polytopes. Several of the...

polytopes | counter-examples | Kostka coefficient | 05E10 | 52B12 | hook formula | Ehrhart polynomial | MATHEMATICS | Mathematics - Combinatorics | Naturvetenskap | Mathematics | Natural Sciences | Matematik

polytopes | counter-examples | Kostka coefficient | 05E10 | 52B12 | hook formula | Ehrhart polynomial | MATHEMATICS | Mathematics - Combinatorics | Naturvetenskap | Mathematics | Natural Sciences | Matematik

Journal Article

Annals of Combinatorics, ISSN 0218-0006, 6/2019, Volume 23, Issue 2, pp. 255 - 262

In 1997 Oda conjectured that every smooth lattice polytope has the integer decomposition property. We prove Oda’s conjecture for centrally symmetric...

52B20 | 52B12 | Smooth lattice polytopes | 52B10 | Integer decomposition property | Central symmetry | 3-dimensional polytopes | Oda’s conjecture | Mathematics | Combinatorics | MATHEMATICS, APPLIED | Oda's conjecture | Naturvetenskap | Natural Sciences | Matematik

52B20 | 52B12 | Smooth lattice polytopes | 52B10 | Integer decomposition property | Central symmetry | 3-dimensional polytopes | Oda’s conjecture | Mathematics | Combinatorics | MATHEMATICS, APPLIED | Oda's conjecture | Naturvetenskap | Natural Sciences | Matematik

Journal Article

Combinatorica, ISSN 0209-9683, 2/2013, Volume 33, Issue 1, pp. 1 - 10

We prove that the number of vertices of a polytope of a particular kind is exponentially large in the dimension of the polytope. As a corollary, we prove that...

52B12 | 05C30 | Mathematics, general | Mathematics | 05C70 | Combinatorics | 05A16 | MATHEMATICS

52B12 | 05C30 | Mathematics, general | Mathematics | 05C70 | Combinatorics | 05A16 | MATHEMATICS

Journal Article

MATHEMATIKA, ISSN 0025-5793, 2019, Volume 65, Issue 3, pp. 763 - 784

We investigate arithmetic, geometric and combinatorial properties of symmetric edge polytopes. We give a complete combinatorial description of their facets. By...

POLYNOMIALS | MATHEMATICS | MATHEMATICS, APPLIED | SEQUENCES | Mathematics | Naturvetenskap | Natural Sciences | Matematik

POLYNOMIALS | MATHEMATICS | MATHEMATICS, APPLIED | SEQUENCES | Mathematics | Naturvetenskap | Natural Sciences | Matematik

Journal Article

Computational Optimization and Applications, ISSN 0926-6003, 4/2019, Volume 72, Issue 3, pp. 561 - 588

Simplex gradients are an essential feature of many derivative free optimization algorithms, and can be employed, for example, as part of the process of...

Simplex gradient | Derivative free optimization | 52B12 | Mathematics | Statistics, general | Optimization | Regular simplex | Numerical optimization | Operations Research/Decision Theory | Convex and Discrete Geometry | Least squares | 65F20 | 90C56 | Well poised | Operations Research, Management Science | Positive bases | 65F35 | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Mathematical optimization | Algebra | Algorithms | Optimization algorithms | Alignment | Mathematical analysis | Linear algebra

Simplex gradient | Derivative free optimization | 52B12 | Mathematics | Statistics, general | Optimization | Regular simplex | Numerical optimization | Operations Research/Decision Theory | Convex and Discrete Geometry | Least squares | 65F20 | 90C56 | Well poised | Operations Research, Management Science | Positive bases | 65F35 | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Mathematical optimization | Algebra | Algorithms | Optimization algorithms | Alignment | Mathematical analysis | Linear algebra

Journal Article

Discrete & Computational Geometry, ISSN 0179-5376, 7/2018, Volume 60, Issue 1, pp. 98 - 114

We show that the Simion type B associahedron is combinatorially equivalent to a pulling triangulation of the type A root polytope known as the Legendre...

Computational Mathematics and Numerical Analysis | Flag complex | 52B12 | Mathematics | Cyclohedron | 52B15 | Primary 52B05 | Type A root polytope | Compressed polytopes | Combinatorics | 05E45 | Secondary 05A15 | Bott–Taubes polytope | Stasheff polytope | Triangulation

Computational Mathematics and Numerical Analysis | Flag complex | 52B12 | Mathematics | Cyclohedron | 52B15 | Primary 52B05 | Type A root polytope | Compressed polytopes | Combinatorics | 05E45 | Secondary 05A15 | Bott–Taubes polytope | Stasheff polytope | Triangulation

Journal Article

Mathematical Programming, ISSN 0025-5610, 11/2016, Volume 160, Issue 1, pp. 149 - 191

Let G be a finite abelian group. This paper is concerned with nonnegative functions on G that are sparse with respect to the Fourier basis. We establish...

Mathematical Methods in Physics | 52B12 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | Theoretical, Mathematical and Computational Physics | 90C22 | 52B55 | Mathematics | Combinatorics | COMPUTER SCIENCE, SOFTWARE ENGINEERING | EXTENDED FORMULATIONS | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MATRICES | HIERARCHIES | OPTIMIZATION | Studies | Decision support systems | Fourier analysis | Semidefinite programming | Mathematical analysis | Functions (mathematics) | Polytopes | Construction | Graphs | Complexity | Mathematical programming

Mathematical Methods in Physics | 52B12 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | Theoretical, Mathematical and Computational Physics | 90C22 | 52B55 | Mathematics | Combinatorics | COMPUTER SCIENCE, SOFTWARE ENGINEERING | EXTENDED FORMULATIONS | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MATRICES | HIERARCHIES | OPTIMIZATION | Studies | Decision support systems | Fourier analysis | Semidefinite programming | Mathematical analysis | Functions (mathematics) | Polytopes | Construction | Graphs | Complexity | Mathematical programming

Journal Article

Mathematical Programming, ISSN 0025-5610, 7/2018, Volume 170, Issue 1, pp. 121 - 140

This is mostly a survey on some mathematical results concerning volumes of polytopes of interest in non-convex optimization. Our motivation is in geometrically...

Polytope | Fixed charge | 52B12 | Vertex packing | Theoretical, Mathematical and Computational Physics | 52B11 | Mathematics | 90C26 | Boolean quadric | 90C27 | Mixed-integer nonlinear optimization | Facility location | 90C10 | Mathematical Methods in Physics | Global optimization | 90C57 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Volume | Numerical Analysis | Spatial branch-and-bound | 90C11 | Monomial | Combinatorics | MATHEMATICS, APPLIED | COMPUTER SCIENCE, SOFTWARE ENGINEERING | BOOLEAN QUADRIC POLYTOPE | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | OPTIMIZATION | INTEGER | Models | Industrial locations | Comparative analysis | Mathematical optimization | Polytopes | Formulations | Computational geometry | Surveying | Boolean algebra | Convexity | Optimization

Polytope | Fixed charge | 52B12 | Vertex packing | Theoretical, Mathematical and Computational Physics | 52B11 | Mathematics | 90C26 | Boolean quadric | 90C27 | Mixed-integer nonlinear optimization | Facility location | 90C10 | Mathematical Methods in Physics | Global optimization | 90C57 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Volume | Numerical Analysis | Spatial branch-and-bound | 90C11 | Monomial | Combinatorics | MATHEMATICS, APPLIED | COMPUTER SCIENCE, SOFTWARE ENGINEERING | BOOLEAN QUADRIC POLYTOPE | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | OPTIMIZATION | INTEGER | Models | Industrial locations | Comparative analysis | Mathematical optimization | Polytopes | Formulations | Computational geometry | Surveying | Boolean algebra | Convexity | Optimization

Journal Article

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