A276110 The number of rotation systems of drawings of the complete graph K_n, where the rotation system describes the clockwise cyclic order of incident edges around each vertex.

1, 2, 5, 102, 11556, 5370725, 7198391729

Offset: 3

Author

Manfred Scheucher, Aug 18 2016

Keywords

• nonn
• more

Comments

The number of realizable order types on n points in the plane (A063666) is exactly the number of rotation systems of straight-line drawings of K_n.

Links

• B. M. Ábrego, O. Aichholzer, S. Fernández-Merchant, T. Hackl, J. Pammer, A. Pilz, P. Ramos, G. Salazar, and B. Vogtenhuber, All Good Drawings of Small Complete Graphs, In Proc. 31st European Workshop on Computational Geometry EuroCG '15, pages 57-60, Ljubljana, Slovenia, 2015.
• A. Arroyo, D. McQuillan, and B. Richter, Drawings of Kn with the same rotation scheme are the same up to Reidemeister moves (Gioan's Theorem), submitted, 2015.
• J. Kynčl, Enumeration of simple complete topological graphs, European Journal of Combinatorics, 30(7):1676-1685, 2009.
• Wikipedia, Rotation Systems

Crossrefs

Coincides with A276109 for n <= 5.

Cf. A000241, A063666.