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- W2998065511 abstract "Abstract Bárány’s colorful generalization of Carathéodory’s Theorem combines geometrical and combinatorial constraints. Kalai–Meshulam (2005) and Holmsen (2016) generalized Bárány’s theorem by replacing color classes with matroid constraints. In this note, we obtain corresponding results in tropical convexity, generalizing the Tropical Colorful Carathéodory Theorem of Gaubert–Meunier (2010). Our proof is inspired by geometric arguments and is reminiscent of matroid intersection. Moreover, we show that the topological approach fails in this setting. We also discuss tropical colorful linear programming and show that it is NP-complete. We end with thoughts and questions on generalizations to polymatroids, anti-matroids as well as examples and matroid simplicial depth." @default.
- W2998065511 created "2020-01-10" @default.
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- W2998065511 date "2022-11-04" @default.
- W2998065511 modified "2023-09-25" @default.
- W2998065511 title "Tropical Carathéodory with Matroids" @default.
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- W2998065511 doi "https://doi.org/10.1007/s00454-022-00446-0" @default.
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