Universal quivers

Sergey Fomin, Kiyoshi Igusa, Kyungyong Lee

备注：: Final version, to appear in Algebraic Combinatorics. 22 pages, 16 figures

英文摘要：

We show that for any positive integer $n$, there exists a quiver $Q$ with $O(n^2)$ vertices and $O(n^2)$ edges such that any quiver on $n$ vertices is a full subquiver of a quiver mutation equivalent to $Q$. We generalize this statement to skew-symmetrizable matrices and obtain other related results. In particular, we show that any quiver is a full subquiver of a quiver mutation equivalent to a quiver of a plabic graph.

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