7 papers · 1 filter
A common generalization to strengthenings of Drisko's Theorem for intersections of two matroids
Eli Berger, Daniel McGinnis
Let and be two matroids on the same ground set . Let be sets which are independent in both and , sati…
A topological product Tverberg Theorem
Andreas F. Holmsen, Grace McCourt, Daniel McGinnis +1
We prove a generalization of the topological Tverberg theorem. One special instance of our general theorem is the following: Let denote the 8-dimensional simplex viewed as an a…
Matroid colorings of KKM covers
Daniel McGinnis
We prove a KKM-type theorem for matroid colored families of set coverings of a polytope. This generalizes Gale's colorful KKM theorem as well as recent sparse-colorful variants by…
Using the KKM theorem
Daniel McGinnis, Shira Zerbib
The KKM theorem, due to Knaster, Kuratowski, and Mazurkiewicz in 1929, is a fundamental result in fixed-point theory, which has seen numerous extensions and applications. In this p…
Ehrhart Bounds for Panhandle and Paving Matroids Through Enumeration of Chain Forests
Danai Deligeorgaki, Daniel McGinnis, Andrés R. Vindas-Meléndez
Panhandle matroids are a specific family of lattice-path matroids corresponding to panhandle-shaped Ferrers diagrams. Their matroid polytopes are the subpolytopes carved from a hyp…
Asymmetric Ramsey properties of randomly perturbed graphs
Emily Heath, Daniel McGinnis
In this note, we investigate for various pairs of graphs the question of how many random edges must be added to a dense graph to guarantee that any red-blue coloring of the…
The Existence and Structure of Universal Partial Cycles
Dylan Fillmore, Bennet Goeckner, Rachel Kirsch +2
A universal partial cycle (or upcycle) for is a cyclic sequence that covers each word of length over the alphabet exactly once -- like a De Bruijn…