A unique polynomial invariant φ_NCP compatible with two cointeracting coproducts on noncrossing partitions is defined, interpreted as counting valid colorations, and linked to Catalan, Stirling, Riordan array, and Faà di Bruno structures.
Biane, Free probability and combinatorics , Proceedings of the international congress of mathematicians, ICM 2002, Beijing, China, August 20–28, 200 2
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Cointeraction on noncrossing partitions and related polynomial invariants
A unique polynomial invariant φ_NCP compatible with two cointeracting coproducts on noncrossing partitions is defined, interpreted as counting valid colorations, and linked to Catalan, Stirling, Riordan array, and Faà di Bruno structures.