### Abstract

We have produced extended series for two-dimensional prudent polygons, based on a transfer matrix algorithm of complexity O(n^{5}), 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.

Original language | English |
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Article number | 095205 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 42 |

Issue number | 9 |

DOIs | |

Publication status | Published - 4 Feb 2009 |

Externally published | Yes |

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## Cite this

*Journal of Physics A: Mathematical and Theoretical*,

*42*(9), [095205]. https://doi.org/10.1088/1751-8113/42/9/095205