On the number of hexagonal polyominoes
Theoretical Computer Science - Random generation of combinatorial objects and bijective combinatorics
Counting polyominoes: a parallel implementation for cluster computing
ICCS'03 Proceedings of the 2003 international conference on Computational science: PartIII
Counting Polycubes without the Dimensionality Curse
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
| Hi-index | 0.00 |
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.