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Open Claude Desktopcombinatorics · partitions · non-crossing
The organizer’s problem statement is available at the official source link.
noncrossing partition
Partition blocks cannot cross in index order
Different blocks may not interleave as a<c in one block and b<d in another with a<b<c<d.
A---D contains B-CA--C crosses B--Dvalid: no crossing blocks
- 1
Place elements in order
Place 1…n in order and assign every element to exactly one block. - 2
Reject crossing blocks
Check that no two blocks have alternating members. - 3
Count valid partitions
Count distinct valid partitions with at most k blocks.
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