Canonical Hopf algebras between QSym and the peak algebra
Sam Hsiao, (University of Michigan)
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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