A transfer matrix approach to the enumeration of plane meanders

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12 Citations (Scopus)

Abstract

A closed-plane meander of order n is a closed self-avoiding curve intersecting an infinite line 2n times. Meanders are considered distinct up to any smooth deformation leaving the line fixed. We have developed an improved algorithm, based on transfer matrix methods, for the enumeration of plane meanders. While the algorithm has exponential complexity, its rate of growth is much smaller than that of previous algorithms. The algorithm is easily modified to enumerate various systems of closed meanders, semi-meanders, open meanders and many other geometries.

Original languageEnglish
Pages (from-to)5953-5963
Number of pages11
JournalJournal of Physics A: Mathematical and General
Volume33
Issue number34
DOIs
Publication statusPublished - 1 Sep 2000
Externally publishedYes

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