A296406 -id:A296406 - cp's OEIS frontend

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

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

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.

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

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

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

a(6) from Manfred Scheucher, Dec 11 2017

A296407 Number of digon-free 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.

Original entry on oeis.org

1, 1, 1, 1, 3, 30, 4509

Offset: 0

Manfred Scheucher, Dec 11 2017

For more information, see A288568.

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

A296412 Number of non-isomorphic digon-free cylindrical arrangements of n pairwise intersecting pseudo-circles on a sphere, in the sense that two cells of the arrangement are separated by each of the pseudo-circles, reduced for mirror symmetry.

Original entry on oeis.org

1, 1, 1, 1, 2, 14, 2131, 3012906

Offset: 0

Manfred Scheucher, Dec 11 2017

For more information, see A296406.

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

A296408 Number of cylindrical connected arrangements of n pseudo-circles on a sphere, in the sense that the union of the pseudo-circles is a connected set and two cells of the arrangement are separated by each of the pseudo-circles, reduced for mirror symmetry.

Original entry on oeis.org

1, 1, 1, 3, 20, 900, 530530

Offset: 0

Manfred Scheucher, Dec 11 2017

For more information, see A288568.

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

A296409 Number of digon-free cylindrical connected arrangements of n pseudo-circles on a sphere, in the sense that the union of the pseudo-circles is a connected set and two cells of the arrangement are separated by each of the pseudo-circles, reduced for mirror symmetry.

Original entry on oeis.org

1, 1, 1, 1, 3, 30, 4477

Offset: 0

Manfred Scheucher, Dec 11 2017

For more information, see A288568.

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

A296410 Number of non-isomorphic digon-free arrangements of n pairwise intersecting pseudo-circles on a sphere, reduced for mirror symmetry.

Original entry on oeis.org

1, 1, 1, 1, 2, 14, 2131, 3012972

Offset: 0

Manfred Scheucher, Dec 11 2017

For more information, see A296406.

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

A296411 Number of non-isomorphic cylindrical arrangements of n pairwise intersecting pseudo-circles on a sphere, in the sense that two cells of the arrangement are separated by each of the pseudo-circles, reduced for mirror symmetry.

Original entry on oeis.org

1, 1, 1, 8, 278, 144395, 436634633

Offset: 0

Manfred Scheucher, Dec 11 2017

For more information, see A296406.

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

a(7) corrected by Manfred Scheucher, May 09 2018

A339177 a(n) is the number of arrangements on n pseudocircles which are NonKrupp-packed.

Original entry on oeis.org

1, 3, 46, 3453, 784504

Offset: 3

Manfred Scheucher, Nov 26 2020

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

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.

S. Felsner and M. Scheucher, Arrangements of Pseudocircles: On Circularizability, Discrete & Computational Geometry, Ricky Pollack Memorial Issue, 64(3), 2020, pages 776-813.
S. Felsner and M. Scheucher, Homepage of Pseudocircles.
C. Medina, J. Ramírez-Alfonsín, and G. Salazar, The unavoidable arrangements of pseudocircles, Proc. Amer. Math. Soc. 147, 2019, pages 3165-3175.
M. Scheucher, Points, Lines, and Circles: Some Contributions to Combinatorial Geometry, PhD thesis, Technische Universität Berlin, 2020.

Cf. A296406 (number of arrangements on pairwise intersecting pseudocircles).
Cf. A006248 (number of arrangements on pseudocircles which are Krupp-packed, i.e., arrangements on pseudo-greatcircles).
Cf. A018242 (number of arrangements on circles which are Krupp-packed, i.e., arrangements on greatcircles).

cp's OEIS Frontend

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.

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A296407 Number of digon-free 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.

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A296412 Number of non-isomorphic digon-free cylindrical arrangements of n pairwise intersecting pseudo-circles on a sphere, in the sense that two cells of the arrangement are separated by each of the pseudo-circles, reduced for mirror symmetry.

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A296408 Number of cylindrical connected arrangements of n pseudo-circles on a sphere, in the sense that the union of the pseudo-circles is a connected set and two cells of the arrangement are separated by each of the pseudo-circles, reduced for mirror symmetry.

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A296409 Number of digon-free cylindrical connected arrangements of n pseudo-circles on a sphere, in the sense that the union of the pseudo-circles is a connected set and two cells of the arrangement are separated by each of the pseudo-circles, reduced for mirror symmetry.

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A296410 Number of non-isomorphic digon-free arrangements of n pairwise intersecting pseudo-circles on a sphere, reduced for mirror symmetry.

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Author

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A296411 Number of non-isomorphic cylindrical arrangements of n pairwise intersecting pseudo-circles on a sphere, in the sense that two cells of the arrangement are separated by each of the pseudo-circles, reduced for mirror symmetry.

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Author

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A339177 a(n) is the number of arrangements on n pseudocircles which are NonKrupp-packed.

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