cp's OEIS Frontend

A090339 Number of pseudoline arrangements with n curves.

%I A090339 #34 Apr 16 2025 19:41:26
%S A090339 1,1,1,1,1,6,43,922,38612,3113660
%N A090339 Number of pseudoline arrangements with n curves.
%C A090339 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.
%C A090339 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.
%H A090339 Stefan Felsner and Jacob E. Goodman, <a href="https://www.csun.edu/~ctoth/Handbook/chap5.pdf">Pseudoline Arrangements</a>, 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.
%H A090339 Lukas Finschi, <a href="http://dx.doi.org/10.3929/ethz-a-004255224">A graph theoretical approach for reconstruction and generation of oriented matroids</a>, (2001). Diss., Mathematische Wissenschaften ETH Zürich, Nr. 14335, 2001. See Table 8.2 on page 165.
%H A090339 Jon Wild and Laurence Reeves, <a href="/A090339/a090339.gif">One of the three configurations for n=8 that cannot be drawn with straight lines</a>
%e A090339 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.
%Y A090339 Cf. A090338.
%K A090339 nonn,more
%O A090339 0,6
%A A090339 _Jon Wild_ and _Laurence Reeves_, Jan 27 2004
%E A090339 Title corrected by _Günter Rote_, Apr 14 2025