A transfer matrix approach to the enumeration of plane meanders

Details A transfer matrix approach to the enumeration of plane meanders A transfer matrix approach to the enumeration of plane meanders

2000-08-11

arxiv.org/abs/cond-mat/0008178v1

Physics

Condensed Matter

Statistical Mechanics

13 pages, 9 eps figures, to appear in J. Phys. A

Scientific paper

10.1088/0305-4470/33/34/301

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.

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