A288568 Number of non-isomorphic connected arrangements of n pseudo-circles on a sphere, in the sense that the union of the pseudo-circles is a connected set, reduced for mirror symmetry.

1, 1, 1, 3, 21, 984, 609423

Offset: 0

Author

N. J. A. Sloane, Jun 13 2017, based on information supplied by Jon Wild on August 31 2016

Keywords

• nonn
• more

Comments

These counts have been reduced for mirror symmetry. Computed up to n=5 by Jon Wild and Christopher Jones and communicated to N. J. A. Sloane on August 31 2016. Definition corrected Dec 10 2017 thanks to Manfred Scheucher, who has computed same result with Stefan Felsner independently.

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). - Manfred Scheucher, Dec 11 2017

See A250001, the main entry for this problem, for further information.

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.

Crossrefs

Cf. A250001, A275923, A275924, A288554-A288568, A296406, A296407-A296412, A006248.

Formula

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

Extensions

a(6) from Manfred Scheucher, Dec 11 2017