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Cell Growth Problems

Published online by Cambridge University Press:  20 November 2018

David A. Klarner
David A. Klarner*
Affiliation:
McMaster University, Hamilton, Ontario
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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.

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 19 , 1967, pp. 851 - 863
Copyright
Copyright © Canadian Mathematical Society 1967

References

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