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using\n[Burnside's lemma](https://en.wikipedia.org/wiki/Burnside%27s_lemma)\nand [Pólya enumeration theorem](https://en.wikipedia.org/wiki/P%C3%B3lya_enumeration_theorem).\n\n\nRequirements\n------------\n\n* Python 3.6+\n\n\nUsage\n-----\n\n``` python\nfrom burnside import *\n\n# Number of different unlabeled 4-vertex graphs (i.e. edge colorings of a 4-clique using 2 colors).\nprint(Clique(4).orbit_count(edge_colors=2))\n\n# Generating function for the number of 4-vertex graphs with a given number of edges.\nprint(Clique(4).generating_function(edge_colors=2))\n\n# Number of different unlabeled 4-vertex tournaments (i.e. ways of directing edges of a 4-clique).\nprint(Clique(4).orbit_count(edge_direction=True))\n\n# Number of bracelets with 8 beads -- 3 white and 5 black.\nprint(Cycle(8, reflection=True).generating_function(vertex_colors=2).extract(3))\n\n# Number of ways to color faces of a cube using exactly 3 colors (each color has to be used at least once).\nprint(Cube().generating_function(face_colors=3).extract(lambda vars: len(vars) == 3))\n\n# Generating function for the number of ways of coloring a cube using 3 exchangeable colors.\nprint(Cube().generating_function(face_colors='xyz', permutable_colors=True))\n\n# Number of ways to place an arrow (pointing at one of the 3 vertices) on each face of a tetrahedron.\nprint(Tetrahedron().orbit_count(face_arrows=3))\n```\n\nSee [test.py](test.py) for more examples.\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fadamsol%2Fburnside-counter","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fadamsol%2Fburnside-counter","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fadamsol%2Fburnside-counter/lists"}