Some New Self-avoiding Walk and Polygon Models

Authors:
Nicholas R. Beaton;Philippe Flajolet;Timothy M. Garoni;Anthony J. Guttmann
Affiliations:
Department of Mathematics and Statistics, The University of Melbourne, VIC 3010 Australia, N.Beaton@pgrad.unimelb.edu.au;(This article is dedicated to the memory of Philippe, who sadly passed away on March 22, 2011, before this paper was completed) Algorithms Project, INRIA-Rocquencourt, 78513 Le Chesnay, France, Ph ...;School of Mathematical Sciences, Monash University, VIC 3800 Australia, tim.garoni@dmonash.edu;(Correspd.) Department of Mathematics and Statistics, The University of Melbourne, VIC 3010 Australia, T.Guttmann@ms.unimelb.edu.au
Venue:
Fundamenta Informaticae - Lattice Path Combinatorics and Applications
Year:
2012

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Abstract

We study the behaviour of prudent, perimeter and quasi-prudent self-avoiding walks and polygons in both two and three dimensions, as well as some solvable subsets. Our analysis combines exact solutions of some simpler cases, careful asymptotic analysis of functional equations which can be obtained in more complicated cases and extensive numerical studies based on exact series expansions for less tractable cases, augmented by long Monte Carlo runs in some cases.