4 papers · 1 filter
Modularity, Extensions and Connectivity in Infinite Matroids
Mattias Ehatamm, Peter Nelson, Fernanda Rivera Omana
We generalize the well-studied notion of a modular pair of a finite matroid to arbitrary families of sets in infinite matroids, and use it to develop the theory of infinite matroid…
Rainbow triangles and the ErdÅs-Hajnal problem in projective geometries
Carolyn Chun, James Dylan Douthitt, Wayne Ge +3
We formulate a geometric version of the ErdÅs-Hajnal conjecture that applies to finite projective geometries rather than graphs, in both its usual 'induced' form and the multicolo…
Composition Direction of Seymour's Theorem for Regular Matroids -- Formally Verified
Martin Dvorak, Tristan Figueroa-Reid, Rida Hamadani +8
Seymour's decomposition theorem is a hallmark result in matroid theory presenting a structural characterization of the class of regular matroids. Formalization of matroid theory fa…
Excluding a line from -representable matroids
Jim Geelen, Peter Nelson, Zach Walsh
For each positive integer and each sufficiently large integer , we show that the maximum number of elements of a simple, rank-, -representable matroid with no…