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Title:Eulerian enumeration and other illustrations of the peak phenomenon

Abstract: I will present actual and conjectural examples of the following peak phenomenon: Given a statement regarding the algebra Qsym of quasisymmetric functions, there is an analagous statement that holds for the subalgebra Pi of peak quasisymmetric functions. The actual examples involve two questions: What can be said about the (Hopf) algebraic structure Pi? When is an element of Pi a symmetric function? Answers in both cases will be analogues of well-known results regarding Qsym. For a less direct example, I will use the Qsym-to-Pi analogy to discuss how one might approach certain conjectures about flag-enumerative invariants (e.g. the cd-index) of Eulerian posets; these posets include face lattices of convex polytopes.

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Last Modified on 25/Feb/02