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3d ed. --, Dover books on intermediate and advanced mathematics, xiii, 321 p. illus.
Book
Linear Algebra and Its Applications, ISSN 0024-3795, 11/2018, Volume 557, pp. 438 - 454
It is known that every lattice polytope is unimodularly equivalent to a face of some reflexive polytope. A stronger question is to ask whether every -polytope... 
Normal polytope | [formula omitted]-polytope | Reflexive dimension | Integer decomposition property | Gorenstein Fano polytope | Reflexive polytope | Finite simple graph | Edge polytope | (0,1)-polytope | MATHEMATICS | MATHEMATICS, APPLIED | GRAPHS
Journal Article
SIAM Journal on Matrix Analysis and Applications, ISSN 0895-4798, 2015, Volume 36, Issue 2, pp. 634 - 655
Journal Article
Discrete Mathematics, ISSN 0012-365X, 06/2018, Volume 341, Issue 6, pp. 1645 - 1661
Journal Article
1995, Graduate texts in mathematics, ISBN 9780387943299, Volume 152, ix, 370
Book
1984, London Mathematical Society lecture note series, ISBN 9780521277396, Volume 90, xv, 112
Book
1967, Pure and applied mathematics, Volume 16., xiv, 456
Book
Discrete Applied Mathematics, ISSN 0166-218X, 2018
Motivated by understanding the quality of tractable convex relaxations of intractable polytopes, Ko et al. gave a closed-form expression for the volume of a... 
Cut polytope | Order polytope | Volume | Counting linear extensions | Bounded treewidth | Correlation polytope | Boolean quadric polytope | Mixed-integer non-linear optimization
Journal Article
Advances in Mathematics, ISSN 0001-8708, 11/2018, Volume 338, pp. 912 - 952
We investigate weighted floating bodies of polytopes. We show that the weighted volume depends on the complete flags of the polytope. This connection is... 
Hyperbolic polytope | Convex floating body of polytope | Total number of flags | Flag simplex | Weighted floating body of polytope | Spherical polytope | CONVEX-BODIES | STABILITY | POLYTOPES | FACES | F-VECTORS | MATHEMATICS | MINIMAL VOLUME PRODUCT | BLASCHKE-SANTALO | AFFINE SURFACE | DIVERGENCE
Journal Article
Annals of Combinatorics, ISSN 0218-0006, 12/2018, Volume 22, Issue 4, pp. 875 - 884
Let $$(P,\le _P)$$ (P,≤P) and $$(Q,\le _Q)$$ (Q,≤Q) be finite partially ordered sets with $$|P|=|Q|=d$$ |P|=|Q|=d , and $$\mathcal {C}(P) \subset \mathbb... 
52B20 | Dual polytope | Order polytope | Volume | 52B05 | Gorenstein Fano polytope | Chain polytope | Mathematics | Reflexive polytope | Combinatorics | Facet | Gorenstein fano polytope | MATHEMATICS, APPLIED | QUADRATIC GROBNER BASES | Information science
Journal Article
DISCRETE & COMPUTATIONAL GEOMETRY, ISSN 0179-5376, 07/2018, 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... 
Bott-Taubes polytope | Type A root polytope | MATHEMATICS | Compressed polytopes | Flag complex | ROOT POLYTOPES | COMPUTER SCIENCE, THEORY & METHODS | Cyclohedron | Stasheff polytope
Journal Article
Bulletin of the Australian Mathematical Society, ISSN 0004-9727, 2/2012, Volume 85, Issue 1, pp. 84 - 104
For a d-dimensional convex lattice polytope P. a formula for the boundary volume vol(partial derivative P) is derived in terms of the number of boundary... 
order polytope | boundary volume | lattice polytope | Birkhoff polytope | reflexive polytope | TORIC VARIETIES | MATHEMATICS | THEOREM | CONVEX POLYTOPES | EHRHART POLYNOMIALS | Mathematics - Combinatorics
Journal Article
Discrete & Computational Geometry, ISSN 0179-5376, 07/2019, pp. 1 - 8
For each d≥3, n≥5, and k1,k2,…,kd-1≥2 with k1+k2+⋯+kd-1≤n-1, we show how to construct a regular d-polytope whose automorphism group is of order 2n and whose... 
Polytopes | Automorphisms
Journal Article
2011, Student mathematical library, ISBN 0821853686, Volume 60., xiii, 314
Book
2015, Graduate studies in mathematics, ISBN 9780821851982, Volume 161, xii, 363
Tropical geometry is a combinatorial shadow of algebraic geometry, offering new polyhedral tools to compute invariants of algebraic varieties. It is based on... 
Tropical geometry | Study and teaching (Graduate) | Geometry, Algebraic
Book
Discrete & Computational Geometry, ISSN 0179-5376, 03/2019, pp. 1 - 14
We show that for all integers m⩾2, and all integers k⩾2, the orthogonal groups O±(2m,F2k) act on abstract regular polytopes of rank 2m, and the symplectic... 
Polytopes | Integers
Journal Article
Mathematische Nachrichten, ISSN 0025-584X, 11/2017, Volume 290, Issue 16, pp. 2619 - 2628
It is known that every integral convex polytope is unimodularly equivalent to a face of some Gorenstein Fano polytope. It is then reasonable to ask whether... 
52B20 | Gröbner basis | normal polytope | 13P10 | Gorenstein Fano polytope | Ehrhart polynomial | poset polytope
Journal Article
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