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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
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
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
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
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
Journal Article
1995, ISBN 9780387943299, Volume 152., ix, 370
Book
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
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
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
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
Journal Article
Discrete & Computational Geometry, ISSN 0179-5376, 4/2019, Volume 61, Issue 3, pp. 653 - 660
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
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
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
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
Journal Article
Computational Optimization and Applications, ISSN 0926-6003, 4/2019, Volume 72, Issue 3, pp. 561 - 588
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
Journal Article
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