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 …

A matroid is an independence structure that also satisfies the exchange property, which is something that independent sets in a graph-theoretic sense do not obey. So in that sense, the …

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, …

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 vene...

Dec 9, 2024 · Also, to me it seems that there's one graph on 3 edges missing from the list, a graph similar to (12) but the loop is on the middle vertex.

Dec 31, 2023 · 0 I know that a regular matroid is one that can be represented by a totally unimodular matrix. I also know that a rank r totally unimodular matrix is a matrix over $\mathbb …

Oct 14, 2024 · I just had a quick question about the definition of a loop for an oriented matroid. This issue stemmed from trying to determine what the sign would be associated to a loop in a …

Do not look at the characteristic polynomial of a matrix to try to understand the characteristic polynomial of a matroid. The proper polynomials to look at would be the Tutte polynomial of a …

Oct 14, 2025 · Questions related to the field of Combinatorics called Matroid Theory. Relevant topics include matroids in Combinatorial Optimization, Lattice Theory, Algebraic Geometry, …

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 …