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A339177 a(n) is the number of arrangements on n pseudocircles which are NonKrupp-packed. 0
1, 3, 46, 3453, 784504 (list; graph; refs; listen; history; text; internal format)



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.


Table of n, a(n) for n=3..7.

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).

Sequence in context: A307292 A307290 A193420 * A000576 A336829 A260882

Adjacent sequences:  A339174 A339175 A339176 * A339178 A339179 A339180




Manfred Scheucher, Nov 26 2020



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Last modified June 15 15:16 EDT 2021. Contains 345049 sequences. (Running on oeis4.)