Affiliation:
1. Dept. of Computer Science, The Technion—Israel Institute of Technology, Haifa 32000, Israel
Abstract
A planar polyomino of size n is an edge-connected set of n squares on a rectangular two-dimensional 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, which counts all the above types of polyominoes. For example, our program computed the number of distinct three-dimensional polycubes of size 18. To the best of our knowledge, this is the first tabulation of this value.
Publisher
World Scientific Pub Co Pte Lt
Subject
Applied Mathematics,Computational Mathematics,Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science
Cited by
13 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献