A008981 Number of immersions of the unoriented circle into the oriented plane with n double points.

1, 2, 5, 21, 102, 639, 4492, 34032, 272252, 2267905, 19502386, 172111844, 1551948268

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• nice
• hard
• more

Comments

See Table 1, column 3 of E. D. Demaine et al. paper. - Parthasarathy Nambi, Jan 22 2010

References

• V. I. Arnold, Topological Invariants of Plane Curves and Caustics, American Math. Soc., 1994, p. 16.

Links

• E. D. Demaine, M. L. Demaine, P. Taslakian and G. T. Toussaint, Sand drawings and Gaussian graphs, Journal of Mathematics and the Arts, 1 (2007), 125-133.
• S. M. Gusein-Zade and F. S. Duzhin, On the number of topological types of plane curves; (Russian) Uspekhi Mat. Nauk 53 (1998), no. 3(321), 197-198. English translation: Russian Mathematical Surveys 53 (1998) 626-627.
• S. M. Gusein-Zade and F. S. Duzhin, Enumeration of plane curves with up to 10 selfintersections, Pascal program and result table, 05 Apr 1998.
• Christoph Lamm, The enumeration of doubly symmetric diagrams for strongly positive amphicheiral knots, arXiv:2410.06601 [math.GT], 2024. See p. 14.

Crossrefs

Cf. A008980, A008982, A008983, A008984, A008985, A054993.

Cf. A172023. - Parthasarathy Nambi, Jan 22 2010

Programs

Pascal

Cf. link.

Extensions

Additional comments from Sergei Duzhin, Nov 11 2000

a(11)-a(12) from Sean A. Irvine, Apr 19 2018