Many important families of matroids may be characterized by the minor-minimal matroids that do not belong to the family; these are called forbidden or excluded minors.

Dec 3, 2025 · Roughly speaking, a matroid is a finite set together with a generalization of a concept from linear algebra that satisfies a natural set of properties for that concept. For …

Miraculously, these 'cryptomorphic axiomatizations' all turn out to give the same object. Matroids are meant to generalize various mathematical objects. I'll give one de nition, and then I'll …

This text introduces matroids by emphasizing geometry, focusing especially on geometric (affine) dependence. Interpreting this approach for finite subsets of a vector space, points in Euclidean …

Feb 21, 2025 · Matroids are relatively recent objects in combinatorics, abstracting classes of structures that initially appear quite disparate. They provide a unifying framework that …

Matroids are combinatorial structures that capture the abstract properties of (linear/algebraic/…) dependence. Formally, a matroid is a pair M = (E, I) of a finite set E, the groundset, and a …

An easy class of matroids is given by the uniform ma-troids. They are determined by a set S and a number k: the independent sets are the subsets I of S with |I| ≤ k.

Aug 1, 2025 · In simple terms, matroids allow us to study collections of sets and check if some sets of items can be combined without losing certain properties. This concept has applications …

These notes are intended to provide a brief introduction to the study of matroids beginning with two basic examples, matroids arising from graphs and matroids coming from matrices.

Dec 21, 2025 · The family of lattice path matroids were introduced by J. Bonin, A. de Mier and M. Noy [BMN03]. This family is closed under all matrix minors (deletions and contraction) and …