A296406 Number of non-isomorphic arrangements of n pairwise intersecting pseudo-circles on a sphere, reduced for mirror symmetry.

1, 1, 1, 2, 8, 278, 145058, 447905202

Offset: 0

Author

Manfred Scheucher, Dec 11 2017

Keywords

• nonn
• more

Comments

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).

Links

• S. Felsner and M. Scheucher Homepage of Pseudocircles
• S. Felsner and M. Scheucher, Arrangements of Pseudocircles: On Circularizability, arXiv:1712.02149 [cs.CG], 2017.
• Yan Alves Radtke, Stefan Felsner, Johannes Obenaus, Sandro Roch, Manfred Scheucher, and Birgit Vogtenhuber, Flip Graph Connectivity for Arrangements of Pseudolines and Pseudocircles, arXiv:2310.19711 [math.CO], 2023. See p. 41.

Crossrefs

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

Formula

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