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COCOON
2011
Springer

Proper n-Cell Polycubes in n - 3 Dimensions

9 years 11 months ago
Proper n-Cell Polycubes in n - 3 Dimensions
A d-dimensional polycube of size n is a connected set of n cubes in d dimensions, where connectivity is through (d−1)-dimensional faces. Enumeration of polycubes, and, in particular, specific types of polycubes, as well as computing the asymptotic growth rate of polycubes, is a popular problem in discrete geometry. This is also an important tool in statistical physics for computations related to percolation processes and branched polymers. In this paper we consider proper polycubes: A polycube is said to be proper in d dimensions if the convex hull of the centers of its cubes is d-dimensional. We prove a formula for the number of polycubes of size n that are proper in (n − 3) dimensions. Lattice animals, polyominoes, directed trees.
Andrei Asinowski, Gill Barequet, Ronnie Barequet,
Added 18 Dec 2011
Updated 18 Dec 2011
Type Journal
Year 2011
Where COCOON
Authors Andrei Asinowski, Gill Barequet, Ronnie Barequet, Günter Rote
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