Signed Tilings by Ribbon L n-Ominoes, n Odd, via Gröbner Bases  

作　　者：Viorel Nitica Viorel Nitica(Department of Mathematics, West Chester University, West Chester, PA, USA)

机构地区：[1]Department of Mathematics, West Chester University, West Chester, PA, USA

出　　处：《Open Journal of Discrete Mathematics》2016年第4期297-313,共17页离散数学期刊（英文）

摘　　要：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.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.

关 键 词：POLYOMINO Replicating Tile L-Shaped Polyomino Skewed L-Shaped Polyomino Signed Tilings Gröbner Basis Coloring Invariants 

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