Polyomino coloring and complex numbers |
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Authors: | Jurijs Kirillovs |
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Affiliation: | aDepartment of Mathematics, University of Latvia, Zellu 8, Riga, LV-1002, Latvia |
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Abstract: | Usually polyominoes are represented as subsets of the lattice . In this paper we study a representation of polyominoes by Gaussian integers. Polyomino is represented by the set Then we consider functions of type from the set of all polyominoes to an abelian group G, given by , where v is prime in (N(v) is the norm of v). Using the arithmetic of the ring we find necessary and sufficient conditions for such a function to be a coloring map. |
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Keywords: | Polyomino tiling Coloring Tileability criteria Gaussian integers |
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