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Documents  52C40 | enregistrements trouvés : 5

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A cube is a matroid over $C^n=\{-1,+1\}^n$ that contains as circuits the usual rectangles of the real affine cube packed in such a way that the usual facets and skew-facets are hyperplanes of the matroid.
How many cubes are orientable? So far, only one: the oriented real affine cube. We review the results obtained so far concerning this question. They follow two directions:
1) Identification of general obstructions to orientability in this class. (da Silva, EJC 30 (8), 2009, 1825-1832).
2) (work in collaboration with E. Gioan) Identification of algebraic and geometric properties of recursive families of non-negative integer vectors defining hyperplanes of the real affine cube and the analysis of this question and of las Vergnas cube conjecture in small dimensions.
A cube is a matroid over $C^n=\{-1,+1\}^n$ that contains as circuits the usual rectangles of the real affine cube packed in such a way that the usual facets and skew-facets are hyperplanes of the matroid.
How many cubes are orientable? So far, only one: the oriented real affine cube. We review the results obtained so far concerning this question. They follow two directions:
1) Identification of general obstructions to orientability in this ...

05B35 ; 52A37 ; 52C40

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The classical Tverberg's theorem says that a set with sufficiently many points in $R^d$ can always be partitioned into m parts so that the (m - 1)-simplex is the (nerve) intersection pattern of the convex hulls of the parts. Our main results demonstrate that Tverberg's theorem is but a special case of a much more general situation. Given sufficiently many points, any tree or cycle, can also be induced by at least one partition of the point set. The proofs require a deep investigation of oriented matroids and order types.
(Joint work with Deborah Oliveros, Tommy Hogan, Dominic Yang (supported by NSF).)
The classical Tverberg's theorem says that a set with sufficiently many points in $R^d$ can always be partitioned into m parts so that the (m - 1)-simplex is the (nerve) intersection pattern of the convex hulls of the parts. Our main results demonstrate that Tverberg's theorem is but a special case of a much more general situation. Given sufficiently many points, any tree or cycle, can also be induced by at least one partition of the point set. ...

05B35 ; 52C40

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Some problems connected with the concatenation operation will be described.

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- xiii; 323 p.
ISBN 978-0-521-84930-2

Localisation : Ouvrage RdC (BOKO)

matroïde orientée # langage de programmation de Haskell # configuration hyper-plan # arrengement en pseudo-ligne # polytope convexe # sphère triangulée

52C40 ; 52C35 ; 52C30 ; 52B11 ; 52-04

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- 80 p.
ISBN 978-0-8218-2769-7

Memoirs of the american mathematical society , 0741

Localisation : Collection 1er étage

géométrie discrète # matroïde orienté # triangulation # polytope # convexité combinatoriale # polytope de Lawrence

52B11 ; 52B35 ; 52C40

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