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math.CO2026
Polytopes with large transversal ratio
Michael Gene Dobbins, Seunghun Lee
The transversal ratio of a polytope is the minimum proportion of vertices of required to intersect each facet of . The weak chromatic number of is the minimum number…
math.CO2025
Homotopy equivalence of Grassmannians and MacPhersonians in rank 3
Michael Gene Dobbins
We confirm a long standing conjecture in the case of rank 3 that MacPhersonians are homotopy equivalent to Grassmannians.
math.CO2024
Colorful Intersections and Tverberg Partitions
Michael Gene Dobbins, Andreas F. Holmsen, Dohyeon Lee
The colorful Helly theorem and Tverberg's theorem are fundamental results in discrete geometry. We prove a theorem which interpolates between the two. In particular, we show the fo…