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A090339 Number of full curvilinear flups with n curves. 5
1, 1, 1, 1, 1, 6, 43, 922, 38612, 3113660 (list; graph; refs; listen; history; text; internal format)



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.


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

Finschi, Lukas, A graph theoretical approach for reconstruction and generation of oriented matroids, (2001). Diss., Mathematische Wissenschaften ETH Z├╝rich, 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


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.


Cf. A090338.

Sequence in context: A290783 A159604 A090338 * A225159 A078810 A114074

Adjacent sequences:  A090336 A090337 A090338 * A090340 A090341 A090342




Jon Wild and Laurence Reeves (l(AT)bergbland.info), Jan 27 2004



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Last modified January 19 20:33 EST 2019. Contains 319310 sequences. (Running on oeis4.)