Abstract
The star graph expansion method for calculating high temperature susceptibility series for the Ising model has been extended to the polymer problem. The generating function for self-avoiding walks on the four-dimensional face-centred cubic lattice has been calculated to ninth order. The series coefficients are analysed for singularities of the form t-1 mod ln tp, predicted by renormalisation group calculations. Good convergence is obtained for values of p in the vicinity of p=1/4, (the renormalisation group prediction) and the authors estimate p=0.24+or-0.03. The critical point (connective constant for the polymer problem) is found to be 22.072+or-0.004.