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The homology group of a tiling introduced by M. Reid is studied for certain topological tilings. As in the planar case, for finite square grids on topological surfaces, the method… Click to show full abstract
The homology group of a tiling introduced by M. Reid is studied for certain topological tilings. As in the planar case, for finite square grids on topological surfaces, the method of homology groups, namely the non-triviality of some specific element in the group allows a ?coloring proof? of impossibility of a tiling. Several results about the non-existence of polyomino tilings on certain square-tiled surfaces are proved in the paper.
Keywords:
polyomino tilings;
homology polyomino;
tilings flat;
flat surfaces;
homology
Journal Title: Applicable Analysis and Discrete Mathematics
Year Published: 2021
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Journal Title: Applicable Analysis and Discrete Mathematics
Year Published: 2021
Link to full text (if available)
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recommendations!