Gill Barequet, Günter Rote, and Mira Shalah:

An improved upper bound on the growth constant of polyiamonds

European Conference on Combinatorics, Graph Theory and Applications (EuroComb 2019), Bratislava, 26–30 August 2019, Editors: Jaroslav Nešetřil and Martin Škoviera, Acta Mathematica Universitatis Comenianae (AMUC) 88 (2019), 429–436.  →BibTeX


A polyiamond is an edge-connected set of cells on the triangular lattice. If T(n) denotes the number of distinct (up to translation) polyiamonds made of n cells. It is known that the limit λT of T(n+1)/T(n) (the growth constant) exists. In this paper, we improve the best upper bound on λT from 4 to 3.6108.

The proof relies on a computer calculation, which was done in the Sage system with a simple script.

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Last update: September 30, 2019.