I have to pair numbers in a circle without crossing chords.
This:
The way to solve this is Catalan Numbers where n = nodes/2
The problem comes with some restrictions. I have to calculate the number of possible combinations without some chords. In the next example there are 8 nodes, so the possible combinations are 14. But with these restrictions the solution is 7:
Example with 8 nodes and restrictions
- 5 with 0
- 6 with 1
- 3 with 6
- 2 with 7
How can I calculate the number of results without combining the restrictions?