Carathéodory, Helly and the others in the max-plus world Export

@misc{citeulike:2647987, abstract = {Carath\'eodory's, Helly's and Radon's theorems are three basic results in discrete geometry. Their max-plus counterparts have been proved by various authors. In this paper, more advanced results in discrete geometry are shown to have also their max-plus 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 max-plus settings.}, archivePrefix = {arXiv}, author = {Gaubert, St\&\#xe9;phane and Meunier, Fr\&\#xe9;d\&\#xe9;ric}, citeulike-article-id = {2647987}, citeulike-linkout-0 = {http://arxiv.org/abs/0804.1361}, citeulike-linkout-1 = {http://arxiv.org/pdf/0804.1361}, day = {8}, eprint = {0804.1361}, keywords = {convexity, discrete, tropical}, month = {Apr}, posted-at = {2008-04-10 06:21:30}, priority = {2}, title = {Carath\'eodory, Helly and the others in the max-plus world}, url = {http://arxiv.org/abs/0804.1361}, year = {2008} }

TY - ELEC ID - citeulike:2647987 L3 - citeulike-article-id:2647987 N2 - Carath\'eodory's, Helly's and Radon's theorems are three basic results in discrete geometry. Their max-plus counterparts have been proved by various authors. In this paper, more advanced results in discrete geometry are shown to have also their max-plus 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 max-plus settings. TI - Carath\'eodory, Helly and the others in the max-plus world KW - convexity KW - discrete KW - tropical AU - Gaubert, Stéphane AU - Meunier, Frédéric PY - 2008/Apr/08/ UR - http://arxiv.org/abs/0804.1361 ER -