TOT 043 1983 Spring S-A5 coloring of k vertices in regular n-gon
Source:
August 18, 2019
Coloringcombinatoricscombinatorial geometryregular polygon
Problem Statement
vertices of a regular -gon are coloured. A colouring is called almost uniform if for every positive integer the following condition is satisfied:
If is a set of m consecutive vertices of and is another such set then the number of coloured vertices of differs from the number of coloured vertices of at most by .
Prove that for all positive integers and () an almost uniform colouring exists and that it is unique within a rotation.(M Kontsevich, Moscow)