login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Number of non-isomorphic arrangements of n pairwise intersecting pseudo-circles on a sphere, reduced for mirror symmetry.
8

%I #15 Nov 09 2023 12:13:52

%S 1,1,1,2,8,278,145058,447905202

%N Number of non-isomorphic arrangements of n pairwise intersecting pseudo-circles on a sphere, reduced for mirror symmetry.

%C The list of arrangements is available online on the Homepage of Pseudocircles (see below) and a detailed description for the enumeration can be found in Arrangements of Pseudocircles: On Circularizability (see below).

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

%H S. Felsner and M. Scheucher, <a href="http://arxiv.org/abs/1712.02149">Arrangements of Pseudocircles: On Circularizability</a>, arXiv:1712.02149 [cs.CG], 2017.

%H Yan Alves Radtke, Stefan Felsner, Johannes Obenaus, Sandro Roch, Manfred Scheucher, and Birgit Vogtenhuber, <a href="https://arxiv.org/abs/2310.19711">Flip Graph Connectivity for Arrangements of Pseudolines and Pseudocircles</a>, arXiv:2310.19711 [math.CO], 2023. See p. 41.

%F a(n) = 2^(\Theta(n^2)). (cf. Arrangements of Pseudocircles: On Circularizability)

%Y Cf. A250001, A275923, A275924, A288554-A288568, A296407-A296412, A006248.

%K nonn,more

%O 0,4

%A _Manfred Scheucher_, Dec 11 2017