Abstract

We apply the method of Gröbner bases to polyomino tilings, following and developing the ideas of Bodini and Nouvel. The emphasis is, in the spirit of the paper M. Muzika Dizdarević, R.~T. Živaljević, \emph{Symmetric polyomino tilings, tribones, ideals and Gröbner bases}, Publ. Inst. Math. \textbf{98} (112) (2015), 1--23., on tiling problems with added symmetry conditions. The main problem studied in the paper covers case of tiling by three-in-line polyominoes, centrally symmetric with respect to the origin.

Keywords: Symmetric Z-tiling; ring of invariants; Gröbner bases.

MSC: 52C20, 13P10

Pages:  281$-$295     

Volume  69 ,  Issue  4 ,  2017