Nestings
Pairs of arcs a < b < c < d with a~d and b~c.
Nestings(partition)
Details
- Defined over `SetPartition` as an expression in `_x`, evaluated by compute-engine — the definition IS the implementation.
- Not yet typed over its carrier: `SetPartition` is a restricted growth string in @enumeratio/domains but a list of BLOCKS here, so the head still takes the bare blocks until the two representations are reconciled.
- The complementary case to Crossings: one arc's span strictly contains the other's. Equidistributed with Crossings over set partitions of [n] (Kasraoui–Zeng), and the noncrossing and nonnesting partitions are each counted by the Catalan numbers.