8 citations · 29 across the 18 of their papers we have counts for
22 papers
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…
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.
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…
Inscribable order types
Michael Gene Dobbins, Seunghun Lee
We call an order type inscribable if it is realized by a point configuration where the extreme points are all on a circle. In this paper, we investigate inscribability of order typ…
Transversals and colorings of simplicial spheres
Joseph Briggs, Michael Gene Dobbins, Seunghun Lee
Motivated from the surrounding property of a point set in introduced by Holmsen, Pach and Tverberg, we consider the transversal number and chromatic number of a simp…
A strong equivariant deformation retraction from the homeomorphism group of the projective plane to the special orthogonal group
Michael Gene Dobbins
This is the third paper in a series on oriented matroids and Grassmannians. We construct a -equivariant strong deformation retraction from the hom…