Gill Barequet, Mira Shalah, and Yufei Zheng, An Improved Lower Bound on the Growth Constant of Polyiamonds, Proc. 23rd Ann. Int. Computing and Combinatorics Conference (COCOON), 50-61, 2017.

Abstract:

A polyiamond is an edge-connected set of cells on the triangular lattice. 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.

Bibtex: 

@inproceedings{BSZ17,
	author = {Gill Barequet and Mira Shalah and Yufei Zheng},  
	title = { textbf{An Improved Lower Bound on the Growth Constant of Polyiamonds}}, 
	booktitle = {Proceedings of the 22nd International Computing and Combinatorics Conference (COCOON)},
	month = {August}, 
	year = {2017},
	venue = {Hong Kong, China},
	pages = {50--61},
}