The growth rate of high-dimensional tree polycubes

Gadi Aleksandrowicz; Gill Barequet

doi:10.1016/j.ejc.2013.06.007

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 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 (2. d - 3.5) e + O (1 / d).

Original language	English
Pages (from-to)	32-38
Number of pages	7
Journal	European Journal of Combinatorics
Volume	35
DOIs	https://doi.org/10.1016/j.ejc.2013.06.007
State	Published - Jan 2014

All Science Journal Classification (ASJC) codes

Discrete Mathematics and Combinatorics

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10.1016/j.ejc.2013.06.007

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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 (2. d - 3.5) e + O (1 / d).",

author = "Gadi Aleksandrowicz and Gill Barequet",

note = "Funding Information: A preliminary version of this paper appeared in [2] . Work on this paper by the two authors has been supported in part by a grant from the Bar-Nir Bergreen Software Technology Center of Excellence .",

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language = "الإنجليزيّة",

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AU - Barequet, Gill

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N2 - 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 (2. d - 3.5) e + O (1 / d).

AB - 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 (2. d - 3.5) e + O (1 / d).

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DO - 10.1016/j.ejc.2013.06.007

M3 - مقالة

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VL - 35

SP - 32

EP - 38

JO - European Journal of Combinatorics

JF - European Journal of Combinatorics

ER -

The growth rate of high-dimensional tree polycubes

Abstract

All Science Journal Classification (ASJC) codes

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