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Showing 1 to 20 of 59 for “"polytopes"”.
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Lattice polytopes with distinct pair-sums
Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2012-11-12T15:48:22Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Milos_Curcic.pdf: 1736474 bytes, checksum: 78919c2db9cb41bd6fc66699c7c32e46 (MD5)
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Root polytopes, triangulations, and subdivision algebras
… algebras in terms of subdivisions of root polytopes, several conjectures of Kirillov about the reduced forms of monomials in the algebras are proved and generalized. Other than a way of understanding Kirillov's algebras, this polytope approach also yields new results about root polytopes, …
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On shellings and subdivisions of convex polytopes
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1992.
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Cluster Structure for Mirkovic-Vilonen Cycles and Polytopes
… of the cluster structure among MV cycles and MV polytopes. In particular, we show the exchange relations correspond to an equation involving MV polytopes. We extend a result of Baumann-Kamnitzer in relating valuations of an MV cycle and the dimension of homomorphism spaces of its associated …
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A Study of the Rigidity of Regular Polytopes
… and plate hinge structures of regular convex polytopes in many dimensions and determine their rigidity.
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Some convergence properties of Minkowski functionals given by polytopes
1 PDF file (vii, 28 pages)
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Classification and enumeration of special classes of posets and polytopes
… aspects of different classes of posets and polytopes. The first part concerns the finite Eulerian posets which are binomial, Sheffer or triangular. These important classes of posets are related to the theory of generating functions and to geometry. Ehrenborg and Readdy [ER2] gave a complete …
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Chiral polytopes arising from almost-simple groups with socle PSL(2, q)
… objects have received more attention than polytopes. Since ancient times, polytopes have been considered with great interest, not only for aesthetic reasons, but also for scientific reasons. More recently, the theory of abstract polytopes, which generalises the concept of classical …
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Bounds on the cardinalities of nearly neighborly and neighborly families of polytopes
A family of polytopes in E$\sp{d}$ is called nearly neighborly if, for every two members of the family, there is a hyperplane which separates them and contains a facet of each. Such a family is called neighborly if every two members of the family have a $(d - 1)$-dimensional intersection. We have …
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Combinatorics of colored factorizations, flow polytopes and of matrices over finite fields
… establish the relationship between volumes of ow polytopes associated to signed graphs and the Kostant partition function. A special case of this relationship, namely, when the graphs are signless, has been studied combinatorially by Postnikov and Stanley and by Baldoni and Vergne using residues. …
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Comparative Analysis of Geometric Random Walks for Sampling in High-Dimensional Convex Polytopes
… λογισμικού του χώρου (Volesti, PolytopeWalk, PolytopeSampler), με την υποστήριξη εξειδικευμένων εργαλείων προεπεξεργασίας (PolyRound, Dingo). Το πειραματικό πλαίσιο κλιμακώνεται συστηματικά: από θεμελιώδη θεωρητικά σχήματα (πυκνοί υπερκύβοι, simplex και πολύτοπα Birkhoff έως 10^4 διαστάσεων) …
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Polytopes, generating functions, and new statistics related to descents and inversions in permutations
… paths. Other parts of this thesis are devoted to polytopes relevant to the descent statistic. One such polytope is a "signed" version of the Pitman-Stanley parking function polytope, which can be viewed as a generalization of the chain polytope of the zigzag poset. We also discuss the family of …
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Contributions to the theory of Ehrhart polynomials
… we study the Ehrhart polynomials of different polytopes. In the 1960's Eugene Ehrhart discovered that for any rational d-polytope P, the number of lattice points, i(P,m), in the mth dilated polytope mP is always a quasi-polynomial of degree d in m, whose period divides the least common multiple …
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Combinatorial aspects of polytope slices
… hypersimplices as slices of hypercubes and edge polytopes. For hypersimplices, the main result is a proof of a conjecture by R. Stanley which gives an interpretation of the Ehrhart h*-vector in terms of descents and excedances. Our proof is geometric using a careful book-keeping of a shelling of …
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Descent Systems, Eulerian Polynomials and Toric Varieties
… give the h-polynomial/h-vector of the simple polytopes known as permutohedra, the convex hull of the Sn -orbit for a generic weight in the weight lattice of Sn . Therefore the Eulerian polynomials give the Betti numbers for certain smooth toric varieties associated with the permutohedra. In …
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Generalized Characteristics Of A Generic Polytope
… We will show that, for symplectic-faced 4-polytopes ∑, we have the existence and local uniqueness of generalized characteristics of ∑. Then, we will show that symplectic-faced polytopes ∑ ⊂ R2n admit only characteristics with piecewise-linear trajectories. Finally, we will extend our …
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Elliptic fibrations among toric hypersurface Calabi-Yau manifolds and mirror symmetry of fibrations
… directly the fibration structure of 4D reflexive polytopes by classifying all the 2D subpolytopes of the 4D polytopes in the Kreuzer and Skarke database of toric Calabi-Yau hypersurfaces. With the classification of the 2D fibers, we then study the mirror symmetry structure of elliptic toric …
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Scissors congruence and K-theory
… of algebraic K-theory. Classically, two polytopes in a manifold X are defined to be scissors congruent if they can be decomposed into finite sets of pairwise-congruent polytopes. We generalize this notion to an abstract problem: given a set of objects and decomposition and congruence …
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Power and limitations of convex formulations via linear and semidefinite programming lifts
… (LP) and semidefinite programming (SDP) lifts of polytopes. For LP lifts the bound we develop applies generally for the nonnegative rank of matrices and we compare our method with existing combinatorial and non-combinatorial techniques. For SDP lifts we focus on so-called equivariant lifts that …
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