Exact meander asymptotics: a numerical check. (English) Zbl 0984.82025
Summary: This note addresses the meander enumeration problem: “count all topologically inequivalent configurations of a closed planar non self-intersecting curve crossing a line through a given number of points”. We review a description of meanders introduced recently in terms of the coupling to gravity of a two-flavored fully-packed loop model (see ibid. 570, 699-712 (2000; Zbl 0984.82030). The subsequent analytic predictions for various meandric configuration exponents are checked against exact enumeration, using a transfer matrix method, with an excellent agreement.
MSC:
| 82B41 | Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics |
| 05C80 | Random graphs (graph-theoretic aspects) |
Keywords:
meander enumerationCitations:
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