2000/04/19 by Iwan Jensen, Anthony J Guttmann, Jensen, Iwan +2
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.stat-mech #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.cond-mat/0004321
8 pages, 4 eps figures
arxiv created 2000/04/19 · openalex publication_date 2000/04/19 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.