A planar polyomino of size n is an edge-connected set of n squares on a rectangular 2-D lattice. Similarly, a d-dimensional polycube (for d ≥ 2) of size n is a connected set of n hypercubes on an orthogonal d-dimensional lattice, where two hypercubes are neighbors if they share a (d -1)-dimensional face. There are also two-dimensional polyominoes that lie on a triangular or hexagonal lattice. In this paper we describe a generalization of Redelmeier's algorithm for counting two-dimensional rectangular polyominoes [Re81], which counts all the above types of polyominoes. For example, our program computed the number of distinct 3-D polycubes of size 18. To the best of our knowledge, this is the first tabulation of this value. © Springer-Verlag Berlin Heidelberg 2006.
CITATION STYLE
Aleksandrowicz, G., & Barequet, G. (2006). Counting d-dimensional polycubes and nonrectangular planar polyominoes. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4112 LNCS, pp. 418–427). Springer Verlag. https://doi.org/10.1007/11809678_44
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