The growth rate of high-dimensional tree polycubes

Authors:
Gadi Aleksandrowicz;Gill Barequet
Affiliations:
-;-
Venue:
European Journal of Combinatorics
Year:
2014

Citing 3
Cited 0

Analytic Combinatorics

Analytic Combinatorics
Counting polyominoes: a parallel implementation for cluster computing

ICCS'03 Proceedings of the 2003 international conference on Computational science: PartIII
Formulae and growth rates of high-dimensional polycubes

Combinatorica

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Abstract

A d-dimensional polycube is a face-connected set of cubes in ddimensions, where the faces are (d-1) dimensional. Fixed polycubes are distinct if they differ in shape or orientation. The cube-adjacency graph of a tree polycube does not have cycles. In this paper we estimate the asymptotic growth rate of d-dimensional tree polycubes at (2d-3.5)e+O(1/d).