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The Auslander–Reiten Components in the Rhombic Picture

For an indecomposable module M over a path algebra of a quiver of type , the Gabriel–Roiter measure gives rise to four new numerical invariants; we call them the multiplicity, and the initial, periodic, and final parts. We describe how these invariants for M and for its dual specify the position of M in the Auslander–Reiten quiver of the algebra.