Signed Tilings by Ribbon <i>L n</i>-Ominoes, <i>n</i> Odd, via Gr&#246;bner Bases

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 Gr &#246; bner 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.