A090339 Number of full curvilinear flups with n curves.

1, 1, 1, 1, 1, 6, 43, 922, 38612, 3113660

Offset

0,6

Comments

a(n) counts the topologically distinct planar configurations of n unbounded curves such that each curve crosses each other curve at exactly one point and no two intersection points coincide.

For n<8, a(n) is identical to A090338(n), where the curves must be straight line segments. But at n=8, we find a(n) includes three configurations that cannot be drawn with straight line segments. The qualification "unbounded" disallows configurations that have an endpoint within an area enclosed by other curves. As in A090338(n), configurations related by mirror symmetry are not counted as distinct.

Links

Table of n, a(n) for n=0..9.

Jean-Luc Baril, Céline Moreira Dos Santos, Pizza-cutter's problem and Hamiltonian path, Mathematics Magazine (2019) Vol. 88, No. 1, 1-9. [This paper appears to say that A090338(9) = 3111341. I believe this is an error, and 3111341 refers to the ninth term of the present sequence. - N. J. A. Sloane, Feb 15 2021]

Finschi, Lukas, A graph theoretical approach for reconstruction and generation of oriented matroids, (2001). Diss., Mathematische Wissenschaften ETH Zürich, Nr. 14335, 2001. See table on page 165.

Jon Wild and Laurence Reeves, One of the three configurations for n=8 that cannot be drawn with straight lines

Example

See illustration for one of the three configurations for n=8 that is not drawable with straight lines and so does not appear in A090338. No further intersections between curves, beyond the ones shown, occur outside the visible portion of the plane.

Crossrefs

Cf. A090338.

Sequence in context: A290783 A159604 A090338 * A225159 A078810 A114074

Adjacent sequences: A090336 A090337 A090338 * A090340 A090341 A090342

Keyword

more,nonn

Author

Jon Wild and Laurence Reeves, Jan 27 2004

Status

approved