5 papers
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…
Structuring Definitions in Mathematical Libraries
Alena Gusakov, Peter Nelson, Stephen Watt
Codifying mathematical theories in a proof assistant or computer algebra system is a challenging task, of which the most difficult part is, counterintuitively, structuring definiti…
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…