On partitions and k-polygons

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Let C be a circle divided into n parts equally. The set of the ends of these parts on C are denoted by S = {P0; P1,....,Pn-1}. Let Ck(n) be the number of incongruent k-polygons inscribed in C, where the vertices of k-polygons are chosen from S. In this note, we shall investigate the generating functions of C4(n) and C5(n).

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