@inproceedings{3d13527dc10a4140b6c1437b2ac9f57c,
title = "Proper n-cell polycubes in n - 3 dimensions",
abstract = "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.",
keywords = "Lattice animals, directed trees, polyominoes",
author = "Andrei Asinowski and Gill Barequet and Ronnie Barequet and G{\"u}nter Rote",
year = "2011",
doi = "10.1007/978-3-642-22685-4\_16",
language = "الإنجليزيّة",
isbn = "9783642226847",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
pages = "180--191",
booktitle = "Computing and Combinatorics - 17th Annual International Conference, COCOON 2011, Proceedings",
note = "17th Annual International Computing and Combinatorics Conference, COCOON 2011 ; Conference date: 14-08-2011 Through 16-08-2011",
}