Universal quivers
Algebraic Combinatorics, Volume 4 (2021) no. 4, pp. 683-702.

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.

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DOI: 10.5802/alco.175
Classification: 13F60,  05C25,  05E16,  16G20,  18G80
Keywords: Quiver mutation, universal quiver, cluster algebra.
Fomin, Sergey 1; Igusa, Kiyoshi 2; Lee, Kyungyong 3

1 Department of Mathematics University of Michigan Ann Arbor MI 48109, USA
2 Department of Mathematics Brandeis University Waltham MA 02454, USA
3 Department of Mathematics University of Alabama Tuscaloosa AL 35487, USA;
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Fomin, Sergey; Igusa, Kiyoshi; Lee, Kyungyong. Universal quivers. Algebraic Combinatorics, Volume 4 (2021) no. 4, pp. 683-702. doi : 10.5802/alco.175. https://alco.centre-mersenne.org/articles/10.5802/alco.175/

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