18 citations · 38 across the 33 of their papers we have counts for
44 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…
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…
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 Erdős-Hajnal problem in projective geometries
Carolyn Chun, James Dylan Douthitt, Wayne Ge +3
We formulate a geometric version of the Erdős-Hajnal conjecture that applies to finite projective geometries rather than graphs, in both its usual 'induced' form and the multicolou…
Minors of matroids represented by sparse random matrices over finite fields
Pu Gao, Peter Nelson
Consider a random matrix over the finite field of order where every column has precisely nonzero elements, and let be the matroid represented by .…
On the density of matroids omitting a complete-graphic minor
Peter Nelson, Sergey Norin, Fernanda Rivera Omana
We show that, if is a simple rank- matroid with no -point line minor and no minor isomorphic to the cycle matroid of a -vertex complete graph, then the ratio $|M| /…