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A272906 Number of topologically-distinct pizza slicings from n chords in general position.

Original entry on oeis.org

1, 1, 2, 5, 19, 130, 1814
Offset: 0

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Author

Jon Hart, May 09 2016

Keywords

Comments

The problem is to cut a disk with n chords, no three of which may meet at a single strictly-interior point. For each such slicing, construct the graph on vertices (pieces of the pizza) connected by edges (line segments separating two pieces). a(n) gives the number of such graphs up to isomorphism.
This is an empirical result, obtained from guided random trials. Independent programs agree up to and including a(5)=130. Term a(6)=1814 is unconfirmed.
A054499, counting chord diagrams, is a loose lower bound.

Examples

			For n=3, there are a(3)=5 topologically distinct slicings from chords in general position. These exclude a sixth configuration found when the three chords meet at a point strictly internal to the pizza.

Links

Crossrefs

Cf. A273280.
Maximum number of regions, A000124(n), found in A090338(n) configurations. Minimum number of regions, n+1, found in A000055(n+1) configurations. Configurations can be partitioned by chord diagram, so A054499 is a (loose) lower bound.

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