Symmetric tilings in the square lattice

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 papercovers case of tiling by three-in-line polyominoes, centrally symmetric with respect to the origin.