%0 Generic %1 ArdilaDevelin2007 %A Ardila, Federico %A Develin, Mike %D 2007 %K Ardila Develin arrangement bijection combinatorics correspondence hyperplane matroid orientation product simplex subdivision tropics %T Tropical hyperplane arrangements and oriented matroids %U http://arxiv.org/abs/0706.2920 %X We study the combinatorial properties of a tropical hyperplane arrangement. We define tropical oriented matroids, and prove that they share many of the properties of ordinary oriented matroids. We show that a tropical oriented matroid determines a subdivision of a product of two simplices, and conjecture that this correspondence is a bijection.

@misc{ArdilaDevelin2007, abstract = { We study the combinatorial properties of a tropical hyperplane arrangement. We define tropical oriented matroids, and prove that they share many of the properties of ordinary oriented matroids. We show that a tropical oriented matroid determines a subdivision of a product of two simplices, and conjecture that this correspondence is a bijection. }, added-at = {2008-12-23T17:26:05.000+0100}, author = {Ardila, Federico and Develin, Mike}, biburl = {https://www.bibsonomy.org/bibtex/2597ba544f947158ed52b996fa3fdae5b/fwd13}, description = {Tropical hyperplane arrangements and oriented matroids}, interhash = {46e80e101dfc164cc51b1f1b02327495}, intrahash = {597ba544f947158ed52b996fa3fdae5b}, keywords = {Ardila Develin arrangement bijection combinatorics correspondence hyperplane matroid orientation product simplex subdivision tropics}, note = {cite arxiv:0706.2920 Comment: 20 pages, 7 figures, best viewed in color}, timestamp = {2008-12-23T17:27:06.000+0100}, title = {Tropical hyperplane arrangements and oriented matroids}, url = {http://arxiv.org/abs/0706.2920}, year = 2007 }