The Growth Rate of High-Dimensional Tree Polycubes

Gadi Aleksandrowicz; Gill Barequet

doi:10.1016/j.endm.2011.09.005

The Growth Rate of High-Dimensional Tree Polycubes

Gadi Aleksandrowicz, Gill Barequet

Computer Science

Technion - Israel Institute of Technology

Research output: Contribution to journal › Article › peer-review

Abstract

A d-dimensional polycube is a (d-1)-face-connected set of cubes in d dimensions. Fixed polycubes are considered distinct if they differ in shape or orientation. The cube-adjacency graph of a tree polycube is a tree. In this paper we investigate the asymptotic growth rate of d-dimensional tree polycubes, and estimate it at (2. d-3.5). e+. O(1/d).

Original language	English
Pages (from-to)	25-30
Number of pages	6
Journal	Electronic Notes in Discrete Mathematics
Volume	38
DOIs	https://doi.org/10.1016/j.endm.2011.09.005
State	Published - 1 Dec 2011

Keywords

Lattice animals
Polyominoes

All Science Journal Classification (ASJC) codes

Discrete Mathematics and Combinatorics
Applied Mathematics

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10.1016/j.endm.2011.09.005

Cite this

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abstract = "A d-dimensional polycube is a (d-1)-face-connected set of cubes in d dimensions. Fixed polycubes are considered distinct if they differ in shape or orientation. The cube-adjacency graph of a tree polycube is a tree. In this paper we investigate the asymptotic growth rate of d-dimensional tree polycubes, and estimate it at (2. d-3.5). e+. O(1/d).",

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AB - A d-dimensional polycube is a (d-1)-face-connected set of cubes in d dimensions. Fixed polycubes are considered distinct if they differ in shape or orientation. The cube-adjacency graph of a tree polycube is a tree. In this paper we investigate the asymptotic growth rate of d-dimensional tree polycubes, and estimate it at (2. d-3.5). e+. O(1/d).

KW - Lattice animals

KW - Polyominoes

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DO - 10.1016/j.endm.2011.09.005

M3 - مقالة

SN - 1571-0653

VL - 38

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EP - 30

JO - Electronic Notes in Discrete Mathematics

JF - Electronic Notes in Discrete Mathematics

ER -

The Growth Rate of High-Dimensional Tree Polycubes

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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