Non-commutative Frobenius characteristic of generalized parking functions : Application to enumeration

Abstract

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.

Keywords

• parking function
• species
• non-commutative symmetric functions
• [info.info-dm] computer science [cs]/discrete mathematics [cs.dm]