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Plane and projective meanders. (English) Zbl 0792.05005
The authors study the combinatorial properties of meanders which are non self-intersecting curves on the Euclidean and projective planes. Arithmetic and asymptotic properties of meandric numbers and various other theoretical and numerical results are presented. Connections with other domains of mathematics are discussed.

05A16Asymptotic enumeration
05A15Exact enumeration problems, generating functions
51E15Affine and projective planes
05E20Group actions on designs, etc. (MSC2000)
Full Text: DOI
[1] Arnol’d, V. I.: Ramified covering CP2 $\to S4$, hyperbolicity and projective topology. Siberian math. J. 29, No. 5, 36-47 (1988)
[2] R. Cori, Private communication, 1990.
[3] Eliashberg, Ya.M.: Estimates of number of fixed points of area preserving transformations, VINITI. Syktyvkar, 104 (1979)
[4] Goulden, I. P.; Jackson, D. M.: Combinatorial enumeration. (1983) · Zbl 0519.05001
[5] Koehler, J. E.: Folding a strip of stamps. J. combin. Theory 5, No. 2, 135-152 (1968) · Zbl 0165.32702
[6] Lando, S. K.; Zvonkin, A. K.: Meanders. Selecta math. Soviet. 11, No. 2, 117-144 (1992) · Zbl 0792.05006
[7] Phillips, A.: Addenda and errata. (September 1988)
[8] S. Plouffe, Private communications, 1992.
[9] Poincaré, H.: Sur un théoème de géomeétrie. Rend. del circ. Mat. Palermo 33, 375-407 (1912)
[10] Rosenstiehl, P.: Planar permutations defined by two intersecting Jordan curves. Graph theory and combinatorics (1984) · Zbl 0551.05004