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A cohomology free description of eigencones in type A, B and C
, 2009
"... Let K be a connected compact Lie group. The triples (O1, O2, O3) of adjoint Korbits such that O1+O2+O3 contains 0 are parametrized by a closed convex polyhedral cone. This cone is denoted Γ(K) and called the eigencone of K. For K simple of type A, B or C we give an inductive cohomology free descrip ..."
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Cited by 4 (1 self)
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Let K be a connected compact Lie group. The triples (O1, O2, O3) of adjoint Korbits such that O1+O2+O3 contains 0 are parametrized by a closed convex polyhedral cone. This cone is denoted Γ(K) and called the eigencone of K. For K simple of type A, B or C we give an inductive cohomology free
The covariogram determines threedimensional convex polytopes
, 2008
"... The cross covariogram gK,L of two convex sets K, L ⊂ R n is the function which associates to each x ∈ R n the volume of the intersection of K with L + x. The problem of determining the sets from their covariogram is relevant in stochastic geometry, in probability and it is equivalent to a particul ..."
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Cited by 8 (4 self)
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K,L determines both K and L when K and L are convex polyhedral cones satisfying certain assumptions. These results settle a conjecture of G. Matheron in the class of convex polytopes. Further results regard the known counterexamples in dimension n ≥ 4. We also introduce and study the notion of synisothetic
NULLCONE FOR THE SYMPLECTIC GROUP AND RELATED COMBINATORICS
, 2009
"... We study the nullcone for the symplectic group with respect to a joint action of the general linear group and the symplectic group. By extracting an algebra over a distributive lattice structure from the coordinate ring of the nullcone, we describe a toric degeneration and standard monomial theory ..."
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of the nullcone in terms of double tableaux and integral points in a convex polyhedral cone.
PrimalDual InteriorPoint Methods for SelfScaled Cones
 SIAM Journal on Optimization
, 1995
"... In this paper we continue the development of a theoretical foundation for efficient primaldual interiorpoint algorithms for convex programming problems expressed in conic form, when the cone and its associated barrier are selfscaled (see [9]). The class of problems under consideration includes li ..."
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Cited by 206 (12 self)
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In this paper we continue the development of a theoretical foundation for efficient primaldual interiorpoint algorithms for convex programming problems expressed in conic form, when the cone and its associated barrier are selfscaled (see [9]). The class of problems under consideration includes
Hilbert Bases, Unimodular Triangulations, and Binary Covers of Rational Polyhedral Cones
 GEOM
, 1999
"... We present a hierarchy of covering properties of rational convex cones with respect to the unimodular subcones spanned by the Hilbert basis. For two of the concepts from the hierarchy we derive characterizations: a description of partitions that leads to a natural integer programming formulation for ..."
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Cited by 21 (0 self)
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We present a hierarchy of covering properties of rational convex cones with respect to the unimodular subcones spanned by the Hilbert basis. For two of the concepts from the hierarchy we derive characterizations: a description of partitions that leads to a natural integer programming formulation
Building and Using Polyhedral Hierarchies
, 1993
"... assure that the apexes of removed cones are not connected. As a result we can reattach one or many cones and retain a convex object. We only remove vertices of degree less than 12. As a result, the hierarchy has logarithmic depth. Computing the hierarchy requires linear time and it can be stored in ..."
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assure that the apexes of removed cones are not connected. As a result we can reattach one or many cones and retain a convex object. We only remove vertices of degree less than 12. As a result, the hierarchy has logarithmic depth. Computing the hierarchy requires linear time and it can be stored
Deciding polyhedrality of spectrahedra
, 2011
"... Abstract. Spectrahedra are linear sections of the cone of positive semidefinite matrices which, as convex bodies, generalize the class of polyhedra. In this paper we investigate the problem of recognizing when a spectrahedron is polyhedral. We generalize and strengthen results of [M. V. Ramana, Pol ..."
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Cited by 3 (0 self)
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Abstract. Spectrahedra are linear sections of the cone of positive semidefinite matrices which, as convex bodies, generalize the class of polyhedra. In this paper we investigate the problem of recognizing when a spectrahedron is polyhedral. We generalize and strengthen results of [M. V. Ramana
DISCRETE AUTOMORPHISM GROUPS OF CONVEX CONES OF FINITE TYPE
, 2009
"... We investigate subgroups of SL(n, Z) which preserve an open nondegenerate convex cone in R n and admit in that cone as fundamental domain a polyhedral cone of which some faces are allowed to lie on the boundary. Examples are arithmetic groups acting on selfdual cones, Weyl groups of certain KacMoo ..."
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Cited by 7 (1 self)
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We investigate subgroups of SL(n, Z) which preserve an open nondegenerate convex cone in R n and admit in that cone as fundamental domain a polyhedral cone of which some faces are allowed to lie on the boundary. Examples are arithmetic groups acting on selfdual cones, Weyl groups of certain Kac
THE HYPERMETRIC CONE IS POLYHEDRAL
, 1993
"... The hypermetric cone Hn is the cone in the space R n(n 1)/2 of all vectors d = (dij) 1 <i< j < _ n satisfying the hypermetric inequalities: El<_i<j<n zjzjdij ~ 0 for all integer vectors z in Z n with El<i<n zi = 1. We explore connections of the hypermetric cone with quadrat ..."
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Cited by 11 (3 self)
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with quadratic forms and the geometry of numbers (empty spheres and Lpolytopes in lattices). As an application, we show that the hypermetric cone Hn is polyhedral.
On the extreme rays of the metric cone
 Canad. J. Math
, 1980
"... Introduction. A classical result in the theory of convex polyhedra is that every bounded polyhedral convex set can be expressed either as the intersection of halfspaces or as a convex combination of extreme points. It is becoming increasingly apparent that a full understanding of a class of convex ..."
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Cited by 25 (3 self)
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Introduction. A classical result in the theory of convex polyhedra is that every bounded polyhedral convex set can be expressed either as the intersection of halfspaces or as a convex combination of extreme points. It is becoming increasingly apparent that a full understanding of a class of convex
Results 31  40
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1,894