Presented By: Combinatorics Seminar - Department of Mathematics
Forks and their uses (combinatorics seminar)
Tucker Ervin, University of Alabama
Mutation-finite quivers --- those mutation-equivalent to only a finite number of quivers --- are relatively well-understood objects. However, their counterpart, mutation-infinite quivers, are not. Using a special type of quiver called a fork, we give two results related to mutation-infinite quivers. First, we prove that a quiver being mutation-equivalent to a finite number of non-forks is a hereditary property, i.e., one preserved by restriction to any full subquiver. Second, using only forks and elementary methods, we show that 3-vertex quivers that are not mutation-equivalent to an acyclic quiver have sign-coherent c-vectors.
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