A Remark on Partitions and Triangles

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Let C be a circle divided into n parts equally. S = {P0,P1,...,Pn-1} denotes the set of the ends of these parts on C. Let C3(n) be the number of incongruent triangles inscribed in C, where the vertices of the triangles are chosen from S. In this note, we shall show a relation between the number C3(n) and the partitions into at most three parts.

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