Equivalence Classes of Full-Dimensional $$0/1$$ 0 / 1 -Polytopes with Many Vertices
نویسندگان
چکیده
منابع مشابه
Low-Dimensional Faces of Random 0/1-Polytopes
holds for the expected value of φk(P ). The threshold for k = 1 has recently been determined in [1]. In particular, these results indicate that the high face densities often encountered in polyhedral combinatorics (e.g., for the cut-polytopes of complete graphs) should be considered more as a phenomenon of the general geometry of 0/1-polytopes than as a feature of the special combinatorics of t...
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For a polytope P , the Chvátal closure P ′ ⊆ P is obtained by simultaneously strengthening all feasible inequalities cx ≤ β (with integral c) to cx ≤ ⌊β⌋. The number of iterations of this procedure that are needed until the integral hull of P is reached is called the Chvátal rank. If P ⊆ [0, 1], then it is known that O(n log n) iterations always suffice (Eisenbrand and Schulz (1999)) and at lea...
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The classification of toric Fano manifolds with large Picard number corresponds to the classification of smooth Fano polytopes with large number of vertices. A smooth Fano polytope is a polytope that contains the origin in its interior such that the vertex set of each facet forms a lattice basis. Casagrande showed that any smooth d-dimensional Fano polytope has at most 3d vertices. Smooth Fano ...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2014
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-014-9630-5