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# Documents  De Loera, Jesus A. | enregistrements trouvés : 3

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## Tverberg-type theorems with altered nerves De Loera, Jesus A. | CIRM H

Multi angle

Research talks;Combinatorics;Geometry

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. ...

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## Triangulations. Structures for algorithms and applications De Loera, Jesus A. ; Rambau, Jörg ; Santos, Francisco | Springer 2010

Ouvrage

- xiii; 535 p.
ISBN 978-3-642-12970-4

Algorithms and computation in mathematics , 0025

Localisation : Ouvrage RdC (DELO)

triangulation # région de polyhèdre # configurations d'ensembles de points # volume # polytôpe secondaire # algorithme

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## Algebraic and geometric ideas in the theory of discrete optimization De Loera, Jesus A. ; Hemmecke, Raymond ; Köppe, Matthias | Society For Industrial And Applied Mathematics;Mathematical Optimization Society 2012

Ouvrage

- xix; 322 p.
ISBN 978-1-611972-43-6

MOS-SIAM series on optimization

Localisation : Ouvrage RdC (DELO)

optimisation # géométrie algébrique # programmation en nombres entiers # géométrie combinatoire

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