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Carathéodory, Helly and the Others in the MaxPlus World
Carathéodory, Helly and the Others in the MaxPlus World,10.1007/s004540099207x,Discrete & Computational Geometry,Stephane Gaubert,Frédéric Meunier
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Carathéodory, Helly and the Others in the MaxPlus World
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Citations: 5
)
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Stephane Gaubert
,
Frédéric Meunier
Carath\'eodory's, Helly's and Radon's theorems are three basic results in discrete geometry. Their maxplus counterparts have been proved by various authors. In this paper, more advanced results in
discrete geometry
are shown to have also their maxplus counterparts: namely, the colorful Carath\'eodory theorem and the Tverberg theorem. A conjecture connected to the Tverberg theorem  Sierksma's conjecture , although still open for the usual convexity, is shown to be true in the maxplus settings.
Journal:
Discrete & Computational Geometry  DCG
, vol. 43, no. 3, pp. 648662, 2010
DOI:
10.1007/s004540099207x
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Citation Context
(1)
...Maxplus or tropical convexity is a subject of great current vitality, see [31,32], [33,34,35,36] for initial references and [37,38,39,40,41,42,43,44,45,
46
] for recent developments...
Stéphane Gaubert
.
Maxplus Algebraic Tools for Discrete Event Systems, Static Analysis, ...
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,
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(
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Sort by:
Citations
(5)
Minimal halfspaces and external representation of tropical polyhedra
(
Citations: 7
)
Stéphane Gaubert
,
Ricardo D. Katz
Journal:
Journal of Algebraic Combinatorics  J ALGEBR COMB
, vol. 33, no. 3, pp. 325348, 2011
The number of extreme points of tropical polyhedra
(
Citations: 6
)
Xavier Allamigeon
,
Stéphane Gaubert
,
Ricardo D. Katz
Journal:
Journal of Combinatorial Theory  JCT
, vol. 118, no. 1, pp. 162189, 2011
Tropical polar cones, hypergraph transversals, and mean payoff games
(
Citations: 2
)
Xavier Allamigeon
,
Stephane Gaubert
,
Ricardo D. Katz
Journal:
Computing Research Repository  CORR
, vol. abs/1004.2, 2010
Entrapment and release of drugs by a strict “onoff” mechanism in pullulan microspheres with pendant thermosensitive groups
(
Citations: 1
)
Gheorghe Fundueanu
,
Marieta Constantin
,
Ionela Oanea
,
Valeria Harabagiu
,
Paolo Ascenzi
,
Bogdan C. Simionescu
Journal:
Biomaterials
, vol. 31, no. 36, pp. 95449553, 2010
Maxplus Algebraic Tools for Discrete Event Systems, Static Analysis, and ZeroSum Games
Stéphane Gaubert
Conference:
Formal Modeling and Analysis of Timed Systems  FORMATS
, pp. 711, 2009