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
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
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
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
- 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).
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