We apply the method of Gr"{o}bner bases to polyomino tilings, following and developing the ideas of Bodini and Nouvel. The emphasis is, in the spirit of the paper M. Muzika Dizdarevi'{c}, R.~T. {Z}ivaljevi'{c}, emph{Symmetric polyomino tilings, tribones, ideals and Gr"{o}bner bases}, Publ. Inst. Math. extbf{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.
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机译：我们遵循和发展Bodini和Nouvel的思想，将Gr “ {o} bner bases的方法应用于多米诺瓷砖，重点是论文M. Muzika Dizdarevi'{c}，R.的精神。 T. v {Z} ivaljevi '{c}， emph {对称的多米诺拼贴，三边形，理想和Gr “ {o} bner bases}，Publ。研究所数学。 textbf {98}（112）（2015），1--23。，关于增加对称条件的平铺问题。本文研究的主要问题涉及通过三列直插式多米诺瓷砖进行平铺的情况，相对于原点中心对称。
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