A007756 Number of irreducible indecomposable spherical curves with n crossings (only ordinary double points), the circle is oriented, the sphere is not oriented (OU case).

0, 0, 1, 1, 2, 3, 11, 38, 156, 638, 2973, 13882, 67868, 338147, 1720303, 8905996, 46774728, 248918004, 1340083514, 7288922610, 40019870539, 221582395052, 1236358849827

Offset: 1

Author

Jean Betrema

Keywords

• nonn
• more

Comments

Old name was "Prime Gaussian (i.e. only ordinary double points) curves with n crossings."

Irreducible means not made disconnected by removal of a vertex (no nugatory crossings).

Indecomposable (or prime) means not made disconnected by cutting two distinct lines.

Links

• J. Betrema, Tait Curves
• R. Coquereaux and J.-B. Zuber, Maps, immersions and permutations, arXiv preprint arXiv:1507.03163 [math.CO], 2015-2016. Also J. Knot Theory Ramifications 25, 1650047 (2016), DOI: 10.1142/S0218216516500474
• C. Ernst, C. Hart, T. Menezes and D. Price, A complete list of minimal diagrams of an oriented alternating knot, J. Knot Theory Ramifications 30, 2150063 (2021). See section 3.1.

Crossrefs

Cf. A008986, A008987, A008988, A008989, A264759, A264760, A264761.

Programs

C

See the J. Betrema C program in the Tait Curves link.

Extensions

Edited by Robert Coquereaux, Nov 23 2015

a(15)-a(16) from Sean A. Irvine, Jan 22 2018

a(17)-a(23) from Brendan McKay, Mar 30 2024