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On Partition Dimension of Generalized Convex Polytopes
Published 2023-01-01“…In this work, we consider convex polytopes in their generalized forms that are En,Sn, and Gn, and we compute upper bounds for the partition dimension of the desired polytopes.…”
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62
Ehrhart Polynomials of a Cyclic Polytopes
Published 2009-10-01Subjects: “…cyclic polytopes…”
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63
The Maximal Number of Vertices of The Reflexive Polytope
Published 2015-04-01“…Finally techniques are used to prove the conjecture |V(P)|≤6^(d/2) of the maximal number of vertices for a simplicialreflexive polytopes of even dimension.…”
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64
Approximate cone factorizations and lifts of polytopes
Published 2016“…In this paper we show how to construct inner and outer convex approximations of a polytope from an approximate cone factorization of its slack matrix. …”
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65
Chain Polytopes and Algebras with Straightening Laws
Published 2016“…It will be shown that the toric ring of the chain polytope of a finite partially ordered set is an algebra with straightening laws on a finite distributive lattice. …”
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Polyhedral Gauss sums, and polytopes with symmetry
Published 2016“…We define certain natural finite sums of nn'th roots of unity, called GP(n)GP(n), that are associated to each convex integer polytope PP, and which generalize the classical 11-dimensional Gauss sum G(n)G(n) defined over Z/nZZ/nZ, to higher dimensional abelian groups and integer polytopes. …”
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70
The inverse moment problem for convex polytopes
Published 2013“…We present a general and novel approach for the reconstruction of any convex d-dimensional polytope P, assuming knowledge of finitely many of its integral moments. …”
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Zero-patterns of polynomials and Newton polytopes
Published 2003“…The bound is related to the number of lattice points in the Newton polytopes of the polynomials, and is optimal to within a factor depending only on the dimension (assuming suitable inequalities hold amongst the relevant parameters). …”
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From cracked polytopes to Fano threefolds
Published 2020“…We construct Fano threefolds with very ample anti-canonical bundle and Picard rank greater than one from cracked polytopes—polytopes whose intersection with a complete fan forms a set of unimodular polytopes—using Laurent inversion; a method developed jointly with Coates–Kasprzyk. …”
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The inverse moment problem for convex polytopes
Published 2011“…The goal of this paper is to present a general and novel approach for the reconstruction of any convex d-dimensional polytope P, from knowledge of its moments. In particular, we show that the vertices of an N-vertex polytope in R^d can be reconstructed from the knowledge of O(DN) axial moments (w.r.t. to an unknown polynomial measure od degree D) in d+1 distinct generic directions. …”
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Linear Programming, the Simplex Algorithm and Simple Polytopes
Published 2010-09-01Subjects: “…Randomized Pivot rule complexity combinational theory of simple polytopes…”
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Covering cross-polytopes with smaller homothetic copies
Published 2024-01-01“…Let $ C_{n} $ be an $ n $-dimensional cross-polytope and $ \Gamma_{p}(C_{n}) $ be the smallest positive number $ \gamma $ such that $ C_{n} $ can be covered by $ p $ translates of $ \gamma C_{n} $. …”
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Quantum Walk on the Generalized Birkhoff Polytope Graph
Published 2021-09-01Subjects: “…generalized Birkhoff polytope…”
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