## Canonical Hopf algebras between QSym and the peak algebra

### Sam Hsiao (University of Michigan)

Abstract: The algebra of quasisymmetric functions may be defined as the
linear span of flag f-vector generating functions F(P) as P ranges over
all graded posets. One might ask if any interesting subalgebras of QSym
arise by restricting P to special families of graded posets. For
example, it is well known that Stembridge's peak algebra arises from
the class of Eulerian posets. I'll discuss an infinite family of
Hopf subalgebras that interpolate between QSym and peak algebra.
These are defined by letting P range over Ehrenborg's k-Eulerian
posets. Many assertions about QSym and the peak algebra, such as
freeness and universality, can be extended to these subalgebras.
Relevance to open questions about flag f-vectors will be discussed.

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