An improved lower bound on the growth constant of polyiamonds

Gill Barequet; Mira Shalah; Yufei Zheng

doi:https://doi.org/10.1007/s10878-018-0336-0

An improved lower bound on the growth constant of polyiamonds

Gill Barequet, Mira Shalah, Yufei Zheng

Technion - Israel Institute of Technology

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

Abstract

A polyiamond is an edge-connected set of cells on the triangular lattice in the plane. In this paper, we provide an improved lower bound on the asymptotic growth constant of polyiamonds, proving that it is at least 2.8424. The proof of the new bound is based on a concatenation argument and on elementary calculus. We also suggest a nontrivial extension of this method for improving the bound further. However, the proposed extension is based on an unproven (yet very reasonable) assumption.

Original language	English
Pages (from-to)	424-438
Number of pages	15
Journal	Journal of Combinatorial Optimization
Volume	37
Issue number	2
DOIs	https://doi.org/10.1007/s10878-018-0336-0
State	Published - 15 Feb 2019

Keywords

Growth constant
Lattice animals
Polyiamonds

All Science Journal Classification (ASJC) codes

Computer Science Applications
Discrete Mathematics and Combinatorics
Control and Optimization
Computational Theory and Mathematics
Applied Mathematics

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AB - A polyiamond is an edge-connected set of cells on the triangular lattice in the plane. In this paper, we provide an improved lower bound on the asymptotic growth constant of polyiamonds, proving that it is at least 2.8424. The proof of the new bound is based on a concatenation argument and on elementary calculus. We also suggest a nontrivial extension of this method for improving the bound further. However, the proposed extension is based on an unproven (yet very reasonable) assumption.

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An improved lower bound on the growth constant of polyiamonds

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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