Perfect colorings of patterns with multiple orbits

Acta Crystallogr A Found Adv. 2019 Nov 1;75(Pt 6):814-826. doi: 10.1107/S2053273319011562. Epub 2019 Oct 7.

Abstract

This paper studies colorings of patterns with multiple orbits, particularly those colorings where the orbits share colors. The main problem is determining when such colorings become perfect. This problem is attacked by characterizing all perfect colorings of patterns through the construction of sufficient and necessary conditions for a coloring to be perfect. These results are then applied on symmetrical objects to construct both perfect and non-perfect colorings.

Keywords: color sharing; multiple orbits; perfect colorings.