An improved lower bound on the growth constant of polyiamonds

Gill Barequet (), Mira Shalah () and Yufei Zheng ()
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Gill Barequet: Technion—Israel Institute of Technology
Mira Shalah: Technion—Israel Institute of Technology
Yufei Zheng: Technion—Israel Institute of Technology

Journal of Combinatorial Optimization, 2019, vol. 37, issue 2, No 2, 424-438

Abstract: 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.

Keywords: Polyiamonds; Lattice animals; Growth constant (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10878-018-0336-0

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