A008988 Number of immersions of oriented circle into unoriented sphere with n double points.

1, 1, 2, 6, 21, 97, 579, 3812, 27328, 206410, 1625916, 13241177, 110859326, 950069179, 8307012899, 73908363060, 667683905600

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• nice
• more

Comments

a(10) = 1625916 by sampling method (to be confirmed, cf. ref. arXiv:1507.03163). - Robert Coquereaux, Nov 23 2015

a(10) = 1625916 confirmed. - Brendan McKay, Mar 29 2024

References

• V. I. Arnold, Topological Invariants of Plane Curves and Caustics, American Math. Soc., 1994, p. 18.
• Guy Valette, A Classification of Spherical Curves Based on Gauss Diagrams, Arnold Math J. (2016) 2:383-405, DOI 10.1007/s40598-016-0049-3.

Links

• R. Coquereaux and J.-B. Zuber, Maps, immersions and permutations, arXiv preprint arXiv:1507.03163 [math.CO], 2015-2016. Also DOI, J. Knot Theory Ramifications 25, 1650047 (2016).

Crossrefs

Cf. A008986, A008987, A008989. First line of triangle A260885.

Programs

Magma

// see A260885

Extensions

a(6)-a(7) from Guy Valette, Feb 09 2004

a(8)-a(9) from Robert Coquereaux and Jean-Bernard Zuber, Jul 21 2015

a(10) from same source added by N. J. A. Sloane, Mar 03 2016

a(11)-a(16) from Brendan McKay, Mar 29 2024