Symmetric Colorings of Regular Polygons

Abstract

It is calculated the number of symmetric \(r\)-colorings of vertices of a regular \(n\)-gon and the number of equivalence classes of symmetric \(r\)-colorings. A coloring is symmetric if it is invariant with respect to some mirror symmetry with an axis crossing the center of polygon and one of its vertices. Colorings are equivalent if we can get one from another by rotating about the polygon center.