Non-commutative Frobenius characteristic of generalized parking functions : Application to enumeration - Jean-Baptiste Priez; Aladin Virmaux (Discrete Mathematics & Theoretical Computer Science, 2015)
We give a recursive definition of generalized parking functions that allows them to be viewed as a species. From there we compute a non-commutative characteristic of the generalized parking function module and deduce some enumeration formulas of structures and isomorphism types. We give as well an interpretation in several bases of non commutative symmetric functions. Finally, we investigate an inclusion-exclusion formula given by Kung and Yan.