TITLE:
Signed Tilings by Ribbon L n-Ominoes, n Odd, via Gröbner Bases
AUTHORS:
Viorel Nitica
KEYWORDS:
Polyomino, Replicating Tile, L-Shaped Polyomino, Skewed L-Shaped Polyomino, Signed Tilings, Gröbner Basis, Coloring Invariants
JOURNAL NAME:
Open Journal of Discrete Mathematics,
Vol.6 No.4,
October
14,
2016
ABSTRACT: 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.