Geodesic
Non-commutative Frobenius characteristic of generalized parking functions : Application to enumeration
Discrete mathematics & theoretical computer science, DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015), DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015) (2015).

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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. 
@article{DMTCS_2015_special_285_a48,
     author = {Priez, Jean-Baptiste and Virmaux, Aladin},
     title = {Non-commutative {Frobenius} characteristic of generalized parking functions : {Application} to enumeration},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)},
     year = {2015},
     doi = {10.46298/dmtcs.2504},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2504/}
}
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Priez, Jean-Baptiste; Virmaux, Aladin. Non-commutative Frobenius characteristic of generalized parking functions : Application to enumeration. Discrete mathematics & theoretical computer science, DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015), DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015) (2015). doi : 10.46298/dmtcs.2504. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2504/

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