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

1, 1, 2, 5, 19, 130, 1814

Offset

0,3

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.

Links

Table of n, a(n) for n=0..6.

David O. H. Cutler, Jonas Karlsson, and Neil J. A. Sloane, Cutting a Pancake with an Exotic Knife, arXiv:2511.15864[math.CO], v3, April 19 2026.

Jon Hart, 2 configurations for n=2 cuts

Jon Hart, 5 configurations for n=3 cuts

Jon Hart, 19 configurations for n=4 cuts

Jon Hart, 130 configurations for n=5 cuts

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

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.

Sequence in context: A341036 A365435 A273280 * A054926 A002786 A379707

Adjacent sequences: A272903 A272904 A272905 * A272907 A272908 A272909

Keyword

nonn,more

Author

Jon Hart, May 09 2016

Status

approved