### Abstract

Meanders form a set of combinatorial problems concerned with the enumeration of self-avoiding loops crossing a line through a given number of points, n. Meanders are considered distinct up to any smooth deformation leaving the line fixed. We use a recently developed algorithm, based on transfer matrix methods, to enumerate plane meanders. This allows us to calculate the number of closed meanders up to n = 48, the number of open meanders up to n = 43, and the number of semi-meanders up to n = 45. The analysis of the series yields accurate estimates of both the critical point and critical exponent, and shows that a recent conjecture for the exact value of the semi-meander critical exponent is unlikely to be correct, while the conjectured exponent value for closed and open meanders is not inconsistent with the results from the analysis.

Original language | English |
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Pages (from-to) | L187-L192 |

Number of pages | 6 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 33 |

Issue number | 21 |

DOIs | |

Publication status | Published - Jun 2000 |

Externally published | Yes |

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## Cite this

*Journal of Physics A: Mathematical and General*,

*33*(21), L187-L192. https://doi.org/10.1088/0305-4470/33/21/101