Mathematical Institute of the Serbian Academy of Sciences and Arts
|Title:||HOMOLOGY OF POLYOMINO TILINGS ON FLAT SURFACES||Journal:||Applicable Analysis and Discrete Mathematics||Issue Date:||1-Jan-2022||Rank:||M22||ISSN:||1452-8630||DOI:||10.2298/AADM210307031L||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:||Combinatorial grids | Flat surfaces | Homology group of tiling | Polyomino||Publisher:||University of Belgrade, School of Electrical Engineering|
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