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math.CO2019
Tropical Carathéodory with Matroids
Georg Loho, Raman Sanyal
Bárány's colorful generalization of Carathéodory's Theorem combines geometrical and combinatorial constraints. Kalai-Meshulam (2005) and Holmsen (2016) generalized Bárány's theorem…
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Face posets of tropical polyhedra and monomial ideals
Georg Loho, Ben Smith
We exhibit several posets arising from commutative algebra, order theory, tropical convexity as potential face posets of tropical polyhedra, and we clarify their inclusion relation…