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.

Source : oai:HAL:hal-01337778v1

Volume: DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)

Section: Proceedings

Published on: January 1, 2015

Submitted on: November 21, 2016

Keywords: parking function,species,non-commutative symmetric functions,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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