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a(n) is the number of arrangements on n pseudocircles which are NonKrupp-packed.
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%I #20 Nov 30 2020 09:01:55

%S 1,3,46,3453,784504

%N a(n) is the number of arrangements on n pseudocircles which are NonKrupp-packed.

%C An arrangement of pseudocircles is a collection of simple closed curves on the sphere which intersect at most twice.

%C In a NonKrupp-packed arrangement every pair of pseudocircles intersects in two proper crossings, no three pseudocircles intersect in a common points, and in every subarrangement of three pseudocircles there exist digons, i.e. faces bounded only by two of the pseudocircles.

%H S. Felsner and M. Scheucher, <a href="https://doi.org/10.1007/s00454-019-00077-y">Arrangements of Pseudocircles: On Circularizability</a>, Discrete & Computational Geometry, Ricky Pollack Memorial Issue, 64(3), 2020, pages 776-813.

%H S. Felsner and M. Scheucher, <a href="https://www3.math.tu-berlin.de/diskremath/pseudocircles">Homepage of Pseudocircles</a>.

%H C. Medina, J. Ramírez-Alfonsín, and G. Salazar, <a href="https://doi.org/10.1090/proc/14450">The unavoidable arrangements of pseudocircles</a>, Proc. Amer. Math. Soc. 147, 2019, pages 3165-3175.

%H M. Scheucher, <a href="https://doi.org/10.14279/depositonce-9542">Points, Lines, and Circles: Some Contributions to Combinatorial Geometry</a>, PhD thesis, Technische Universität Berlin, 2020.

%Y Cf. A296406 (number of arrangements on pairwise intersecting pseudocircles).

%Y Cf. A006248 (number of arrangements on pseudocircles which are Krupp-packed, i.e., arrangements on pseudo-greatcircles).

%Y Cf. A018242 (number of arrangements on circles which are Krupp-packed, i.e., arrangements on greatcircles).

%K nonn,hard,more

%O 3,2

%A _Manfred Scheucher_, Nov 26 2020