Séminaire Lotharingien de Combinatoire, 91B.87 (2024), 12 pp.
Tucker J. Ervin, Blake Jackson, Kyungyong Lee and Son Dang Nguyen
Geometry of C-Matrices for Mutation-Infinite Quivers
Abstract.
The set of forks is a class of quivers introduced by M. Warkentin,
where every connected mutation-infinite quiver is mutation equivalent
to infinitely many forks. Let Q be a fork with n vertices, and
w be a fork-preserving mutation sequence.
We show that every c-vector of Q obtained from w is a solution
to a quadratic equation of the form
where qij is the number of arrows between the
vertices i and j in Q.
From the proof of this result, when Q is a rank 3 mutation-cyclic
quiver, every c-vector of Q is a solution to a quadratic equation
of the same form.
Received: November 15, 2023.
Accepted: February 15, 2024.
Final version: April 1, 2024.
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