A matroid gives a general description of those problems where a greedy algorithm provides an optimal solution. Intuitively, they state that you can build a solution step-by-step (this is given by two of the …

Dec 13, 2023 · 3 Well, I think so, and it is less or more equivalent to the basis exchange theorem (which I reinvented answering your question, but looking for a reference to the matroid union theorem I …

Dec 12, 2019 · A highlight of oriented matroid theory is the combinatorial formula for the Pontryagin classes of a triangulated manifold, obtained by Gelfand and MacPherson. Gelfand, MacPherson - …

Oct 11, 2023 · The relation between the closure and the contraction of a matroid M. Ask Question Asked 2 years, 4 months ago Modified 2 years, 3 months ago

Jan 30, 2024 · A simple matroid is determined by its lattice of cyclic subsets (like the lattice of flats, loops and parallel elements are not detected). I don't know when the lattice of cyclic subsets is geometric. …

Jan 3, 2024 · Vertices of Matchings in bipartite Graph are Matroid Ask Question Asked 2 years, 1 month ago Modified 2 years, 1 month ago

Why is what you gave not a category-theoretic definition of a matroid? I would think of a matroid as structure on E, just like a group or a vector space. Even to a category theorist, such a structure …

Dec 13, 2023 · A Matroid Exchange Property Ask Question Asked 2 years, 2 months ago Modified 2 years, 2 months ago

Jul 18, 2021 · As a relatively new abstraction, matroids clearly enjoy a rich theory unto themselves and also offer a viewpoint that suggests interesting analogies and clarifies aspects of the foundations of …

Oct 14, 2023 · Why every component of a loopless matroid is flat? I know that the rank of a loop in a matroid is zero and I read that: A loop is an element of a matroid that is not contained in any …