Cell Growth Problems
Cell Growth Problems
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细胞生长问题
DOI：
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发表时间：
1967
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通讯作者：
D. Klarner
中科院分区：
文献类型：
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作者：
D. Klarner
正方形网格是笛卡尔坐标为整数的平面上所有点的集合。正方形格子是由单位正方形的边界点和内点组成的点集，单位正方形的顶点在格点上。N-Omino是n个单元的并，它是连通的且没有有限割集。所有n元的集合，Rn是每个n的无限集合；然而，我们感兴趣的是两个有限等价类集合的元素，它们在Rn的元素上定义如下：Rn的两个元素属于相同的等价类(I)在Sn中，或(Ii)在Tn中，如果一个元素可以通过(I)平移或(Ii)平面的平移、旋转和反射转换成另一个。
The square lattice is the set of all points of the plane whose Cartesian coordinates are integers. A cell of the square lattice is a point-set consisting of the boundary and interior points of a unit square having its vertices at lattice points. An n-omino is a union of n cells which is connected and has no finite cut set. The set of all n-ominoes, Rn is an infinite set for each n; however, we are interested in the elements of two finite sets of equivalence classes, Sn and Tn , which are defined on the elements of Rn as follows: Two elements of Rn belong to the same equivalence class (i) in Sn , or (ii) in Tn , if one can be transformed into the other by (i) a translation or (ii) by a translation, rotation, and reflection of the plane.