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Let $A$ be a finite set. Let $B$ be a family of subsets of $A$. We are interested in a matroid with a minimum rank such that every element of $B$ is independent. The answer is obvious - a uniform ...

A linear program is the problem of optimizing an linear objective function within some polytope $A$ over $\mathbf R^n$. My question is motivated by the question of when a linear programming problem ...

So, I'll break this post into two questions. Both concern 3-uniform hypergraphs. A 3-uniform hypergraph $H=(V,E)$ consists of a set of vertices $V$ and a set of edges $E$, where each edge $e\in E$ is ...