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 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
Stefan Felsner and Jacob E. Goodman, Pseudoline Arrangements, Chapter 5 of Handbook of Discrete and Computational Geometry, 3rd edition, Jacob E. Goodman, Joseph O'Rourke, and Csaba D. Tóth, editors, CRC Press, 2017.
Lukas Finschi, A graph theoretical approach for reconstruction and generation of oriented matroids, (2001). Diss., Mathematische Wissenschaften ETH Zürich, Nr. 14335, 2001. See Table 8.2 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
KEYWORD
nonn,more
AUTHOR
Jon Wild and Laurence Reeves, Jan 27 2004
EXTENSIONS
Title corrected by Günter Rote, Apr 14 2025
STATUS
approved