Abstract
Let Q be a 3-Kronecker quiver (i.e., two vertices and three arrows having the same starting and ending vertices). The dimension vectors of the indecomposable regular representations X such that |X| = |τiX| will be studied using the Fibonacci numbers, where |X| denotes the length of X and τ denotes the Auslander–Reiten translation. The quasi-lengths of the indecomposable regular representations with dimension vectors (m, m) and (2m, m) will also be discussed.
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