Abstract
We define the set of meandering curves and we partition this set into three classes, corresponding to the cases where neither, one or both extremities of the curve are covered by its arcs. We present enumerative results for each one of these classes and we associate these results with enumerating sequences for other known meandering curves.
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References
Arnold V.I.: The branched covering of \({CP^2 \to S^4}\) , hyperbolicity and projective topology. Sib. Math. J. 29(5), 717–726 (1988)
Barraud J., Panayotopoulos A., Tsikouras P.: Properties of closed meanders. Ars Comb. 67, 181–197 (2003)
Jensen I.: A transfer matrix approach to the enumeration of plane meanders. J. Phys. A 33, 5953–5963 (2000)
Hoffman K., Mehlhorn K., Rosenstiehl P., Tarjan R.: Sorting Jordan sequences in linear time using level-linked search trees. J. Inf. Control 68, 170–184 (1986)
Koehler J.E.: Folding a strip of stamps. J. Comb. Theory 5, 135–152 (1968)
Lando S., Zvonkin A.: Plane and projective meanders. Theor. Comput. Sci. 117, 227–241 (1993)
Legendre S.: Foldings and meanders. Aust. J. Comb. 58(2), 275–291 (2014)
Lunnon W.: A map-folding problem. Math. Comp. 22, 193–199 (1968)
Panayotopoulos A., Tsikouras P.: Properties of meanders. J. Comb. Math. Comb. Comput. 46, 181–190 (2003)
Sawada J., Li R.: Stamp foldings, semi-meanders, and open meanders: fast generation algorithms. Electron. J. Comb. 19(2), #P43 (2012)
Sloane, N.: The online encyclopedia of integer sequences. Published electronically at http://oeis.org
Strabo, Geography, Boox XII, Ch. 8, 577
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Panayotopoulos, A., Vlamos, P. Partitioning the Meandering Curves. Math.Comput.Sci. 9, 355–364 (2015). https://doi.org/10.1007/s11786-015-0234-0
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DOI: https://doi.org/10.1007/s11786-015-0234-0