Parking functions and tridendriform bialgebra structures

Emily Burgunder (Warsaw)

Wednesday 5th November, 2008 16:00-17:00 214

Abstract

A Parking function is a sequence of non negative integers majorated by a permutation of {1,...,n}. We construct a family of shuffle bialgebras on some combinatorial Hopf algebras and we show that this construction can be extended to Parking functions. This shuffle structure induces a Hopf algebra structure, and on the Parking functions it is exactly the canonical one. We show that as a tridendriform bialgebra the latter is cofree and we unravel the structure of its primitives: it is a variation of a Gerstenhaber-Voronov algebra. Then, we construct a family a q-tridendriform algebras and under a cofreeness condition we are able to unravel the structure of their primitives.

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