Abstract. We have produced extended series for two-dimensional prudent polygons, based on a transfer matrix algorithm of complexity O(n⁵), for a series of n-step polygons. For prudent polygons in two dimensions we find the growth constant to be smaller than that for the corresponding walks, and by considering three distinct subclasses of prudent walks and polygons, we find that the growth constant for polygons varies with class, while for walks it does not. We give exact values for the critical exponents γ and α for walks and polygons, respectively. We have extended the definition of prudent walks to three dimensions and produced series expansions, using a back-tracking algorithm, for both walks and polygons. In the three-dimensional case we estimate the growth constant for both walks and polygons and also estimate the usual critical exponents γ, ν and α.

PACS numbers: 05.50.+q, 05.70.Jk, 02.10.Ox

Print publication: Issue 9 (6 March 2009)
Received 17 October 2008, in final form 3 January 2009
Published 4 February 2009