## 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
### Abstract

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
`λ`_{T}
of `T`(`n`+1)/`T`(`n`) (the *growth
constant*) exists. In this paper, we improve the best upper
bound on `λ`_{T}
from 4 to 3.6108.

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

Last update: September 30, 2019.