Signed Tilings by Ribbon L n-Ominoes, n Odd, via Gröbner BasesReport as inadecuate




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We show that a rectangle can be signed tiled by ribbon L n-ominoes, n odd, if and only if it has a side divisible by n. A consequence of our technique, based on the exhibition of an explicit Gröbner basis, is that any k-inflated copy of the skewed L n-omino has a signed tiling by skewed L n-ominoes. We also discuss regular tilings by ribbon L n-ominoes, n odd, for rectangles and more general regions. We show that in this case obstructions appear that are not detected by signed tilings.

KEYWORDS

Polyomino, Replicating Tile, L-Shaped Polyomino, Skewed L-Shaped Polyomino, Signed Tilings, Gröbner Basis, Coloring Invariants

Cite this paper

Nitica, V. 2016 Signed Tilings by Ribbon L n-Ominoes, n Odd, via Gröbner Bases. Open Journal of Discrete Mathematics, 6, 297-313. doi: 10.4236-ojdm.2016.64025.





Author: Viorel Nitica

Source: http://www.scirp.org/



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