# Bounds for the Connective Constant of the Hexagonal Lattice

#### by

## Sven Erick Alm and Robert Parviainen

#### Uppsala University

In
*J. Phys. A: Math. Gen., volume 37, issue 3 (2004), pages 549 - 560
*

pdf

### Abstract

We give improved bounds for the connective constant of the hexagonal lattice.
The lower bound is found using Kesten's method of irreducible bridges,
and by determining generating functions for bridges on one-dimensional
lattices. The upper bound is obtained as the largest eigenvalue of a
certain transfer matrix.

Using a relation between the hexagonal and (3.12.12) lattices, we also give bounds for the connective constant of the latter lattice.

2010-03-04, Sven Erick Alm, sea@math.uu.se