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

0,4

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

Table of n, a(n) for n=0..6.

S. Felsner and M. Scheucher Homepage of Pseudocircles

S. Felsner and M. Scheucher, Arrangements of Pseudocircles: On Circularizability, arXiv:1712.02149 [cs.CG], 2017.

Formula

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

Crossrefs

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

Sequence in context: A327037 A144621 A288567 * A111433 A111435 A111438

Adjacent sequences: A288565 A288566 A288567 * A288569 A288570 A288571

Keyword

nonn,more

Author

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

Extensions

a(6) from Manfred Scheucher, Dec 11 2017

Status

approved