Dizdarevic, M.M., Timotijevic, M. and Zivaljevic, R.T. (2016) Signed Polyomino Tilings by n-in-Line Polyominoes and Gröbner Bases. Publications de l’Institut Mathematique, Nouvelle série, 99, 31-42.

has been cited by the following article:

• 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.