Abstract
This paper investigates the minimal exponent matrix and minimal weight functions of the admissible quiver. Found limitations for the sum of the elements of exponent matrix with a single quiver and a limitation for the sum of the elements the minimal exponent matrix with quiver which has a loop in each the top. It is shown that reducing the weight of a simple quiver cycle, can lead to an increase in the sum of elements of the exponent matrix from which you get a quiver. An example is given that refutes the hypothesis that that for a quiver with a loop in each vertex, the weight function with the weight of all simple cycles equal to 2 is minimal. It is proved that a rigid quiver is obtained from a minimal exponent matrix.
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