On the Number of p4-tilings by an N-omino
On the Number of p4-tilings by an N-omino
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关于 N-omino 的 p4-平铺数量
DOI：
10.1142/s0218195919400016
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
Kazuyuki Amano and Yoshinobu Haruyama
中科院分区：
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作者：
Yoshiki Nakamura;Kazuyuki Asada;Naoki Kobayashi;Ryoma Sin'ya;Takeshi Tsukada;金澤慶明，西田直樹，酒井正彦;Kazuyuki Amano and Yoshinobu Haruyama
如果平铺中的每一对副本都具有将一个副本映射到另一个副本的平铺的对称性，则由多项式的副本构成的平面平铺称为等面体。我们证明了，对于每个-Omino(即，由单元组成的多项式)，由90度旋转产生的非等价等面体平铺的数目，即所谓的p4-平铺或四分之一圈平铺，是由一个常数(独立于)限定的。证明依赖于对多项式的边界词的因式分解的分析。我们还给出了一个多项式的例子，该多项式有三个不等价的p4平铺。
A plane tiling by the copies of a polyomino is called isohedral if every pair of copies in the tiling has a symmetry of the tiling that maps one copy to the other. We show that, for every-omino (i.e., polyomino consisting ofcells), the number of non-equivalent isohedral tilings generated by 90 degree rotations, so called p4-tilings or quarter-turn tilings, is bounded by a constant (independent of). The proof relies on the analysis of the factorization of the boundary word of a polyomino. We also show an example of a polyomino that has three non-equivalent p4-tilings.