Abstract. We use new algorithms, based on the finite lattice method of series expansion, to extend the enumeration of self-avoiding walks and polygons on the triangular lattice to length 40 and 60, respectively. For self-avoiding walks to length 40 we also calculate series for the metric properties of mean-square end-to-end distance, mean-square radius of gyration and the mean-square distance of a monomer from the end points. For self-avoiding polygons to length 58 we calculate series for the mean-square radius of gyration and the first 10 moments of the area. Analysis of the series yields accurate estimates for the connective constant of triangular self-avoiding walks, μ = 4.150 797 226(26), and confirms to a high degree of accuracy several theoretical predictions for universal critical exponents and amplitude combinations.

Key words: critical exponents and amplitudes (theory); series expansions

Received 19 August 2004, accepted for publication 14 October 2004
Published 25 October 2004