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math.CO2025
Colorful circuits and colorful topes in oriented matroids
Minho Cho, Seunghun Lee, Frédéric Meunier
We provide a short proof of a conic version of the colorful Carathéodory theorem for oriented matroids. Holmsen's extension of the colorful Carathéodory theorem to oriented matroid…
math.CO2025
Matroids, intersecting bases, and Borsuk property
Gyivan López-Campos, Frédéric Meunier, Jorge L. Ramírez Alfonsín
A subset of has the Borsuk property if it can be decomposed into at most parts of diameter smaller than . This is an important geometric property, inspir…