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Crossings

Pairs of arcs a < b < c < d with a~c and b~d.

Crossings(partition)

Domain: Set partition statistics

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.
  • Read off the standard arc representation: within each block, consecutive elements are linked, and a crossing is two arcs whose spans interleave rather than nest or sit apart.

Examples