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

1, 3, 46, 3453, 784504

Offset: 3

Author

Manfred Scheucher, Nov 26 2020

Keywords

• nonn
• hard
• more

Comments

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.

Links

• 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.

Crossrefs

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).