

A272906


Number of topologicallydistinct pizza slicings from n chords in general position.


2




OFFSET

0,3


COMMENTS

The problem is to cut a disk with n chords, no three of which may meet at a single strictlyinterior 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.


LINKS



EXAMPLE

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.


CROSSREFS

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.


KEYWORD

nonn,more


AUTHOR



STATUS

approved



