Preparing an exam, I'm looking for examples of matroids and maybe hints or references on proves that they are. (what I already know are representable matroids and graphic matroids)
2026-03-25 05:59:50.1774418390
Examples of Matroids
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There is the uniform matroid $U_{n,k}$ on ground set $[n] = \{1,2,\dots,n\}$ which has bases $\binom{[n]}{k}$ (the $k$-element subsets of $[n]$). Or equivalently a subset of $[n]$ is independent if and only if it has fewer than $k$ elements.
Given a bipartite graph $G$ with vertex set partitioned as $A \sqcup B$ there is the transversal matroid on ground set $A$ where independent sets are endpoints in $A$ of edges in matchings. Or equivalently bases are endpoints in $A$ of edges of maximum size matchings.
To show either of these examples above are matroids just follow your nose and verify the matroids axioms for either bases or independent sets (or both for practice).