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Apologies for this very basic question in matroid theory, but I could not find anything about it online after a bit of searching. There is a well-known bijective correspondence ("cryptomorphism&...

Let $C$ be a simplicial complex on a finite set $V$: that means $C$ is a collection of subsets of $V$ such that if $\sigma\in C$ and $\tau\subseteq \sigma$, then $\tau\in C$. The Alexander dual $D(C)$ ...

I am looking for Sperner-type lemmas where: The colors are on the edges (1-dimensional simplices) - rather than on the vertices; The target is a fully-colored vertex (a vertex adjacent to n edges of ...

Let $G$ be a simple graph on a finite vertex set. The clique complex $X(G)$ is the simplicial complex whose faces are complete subgraphs of $G$, and the independence complex $I(G)$ is the simplicial ...

So, I know that one can apply the strong LP duality theorem to specific instances of maximum flow problems to recover some nontrivial theorems in combinatorics, such as Hall's theorem, Koenig's ...