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

3,2

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

Table of n, a(n) for n=3..9.

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.

Sequence in context: A208209 A276267 A215845 * A136106 A122696 A237267

Adjacent sequences: A276107 A276108 A276109 * A276111 A276112 A276113

Keyword

nonn,more

Author

Manfred Scheucher, Aug 18 2016

Status

approved