A new look at Pieri Operators on Posets.

Nantel Bergeron
York University

Abstract: In this talk we will adapt to classic Hopf algebras the theory of
Aguiar on infinitesimal Hopf algebra. This will allow us to see our work on
Pieri operations on poset with a new perspective.
We introduce the concept of  the Hopf algebra,  HP,  of a poset,  P.  Then
defining Pieri operations on the Poset  P  will naturally induce (via
universal properties) a  Hopf-morphism,   K,  from  HP to the Hopf ,  Qsym,
of quasi-symmetric functions.
If time allow, we will see that the peak algebra of Stembridge is then the
natural Eulerian subalgebra of Qsym.