Universal amplitude combinations for self-avoiding walks, polygons and trails

The authors give exact relations for a number of amplitude combinations that occur in the study of self-avoiding walks, polygons and lattice trails. In particular, they elucidate the lattice-dependent factors which occur in those combinations which are otherwise universal, show how these are modified for oriented lattices, and give new results for amplitude ratios involving even moments of the area of polygons. They also survey numerical results for a wide range of amplitudes on a number of oriented and regular lattices, and provide some new ones.