Ar. Conway et al., ALGEBRAIC TECHNIQUES FOR ENUMERATING SELF-AVOIDING WALKS ON THE SQUARE LATTICE, Journal of physics. A, mathematical and general, 26(7), 1993, pp. 1519-1534
We describe a new algebraic technique for enumerating self-avoiding wa
lks on the rectangular lattice. The computational complexity of enumer
ating walks of N steps is of order 3N/4 times a polynomial in N, and s
o the approach is greatly superior to direct counting techniques. We h
ave enumerated walks of up to 39 steps. As a consequence, we are able
to accurately estimate the critical point, critical exponent, and crit
ical amplitude.