Prudent Self-Avoiding Walks

doi:10.3390/e10030309

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Entropy 2008, 10(3), 309-318; doi:10.3390/e10030309

Article

Prudent Self-Avoiding Walks

John C. Dethridge and Anthony J. Guttmann *

ARC Centre of Excellence for Mathematics and Statistics of Complex Systems, Department of Mathematics and Statistics, The University of Melbourne, Victoria 3010, Australia

* Author to whom correspondence should be addressed.

Received: 17 May 2008 / Accepted: 9 September 2008 / Published: 24 September 2008

(This article belongs to the Special Issue Concepts of Entropy and Their Applications - Papers presented at the Meeting at University of Melbourne, 26 November - 11 December 2007)

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Abstract: We have produced extended series for prudent self-avoiding walks on the square lattice. These are subsets of self-avoiding walks. We conjecture the exact growth constant and critical exponent for the walks, and show that the (anisotropic) generating function is almost certainly not differentiably-finite.

Keywords: self-avoiding walks; prudent walks; D-finite

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Cite This Article

MDPI and ACS Style

Dethridge, J.C.; Guttmann, A.J. Prudent Self-Avoiding Walks. Entropy 2008, 10, 309-318.

AMA Style

Dethridge J.C., Guttmann A.J. Prudent Self-Avoiding Walks. Entropy. 2008; 10(3):309-318.

Chicago/Turabian Style

Dethridge, John C.; Guttmann, Anthony J. 2008. "Prudent Self-Avoiding Walks." Entropy 10, no. 3: 309-318.

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