UW Combinatorics and Geometry Seminar: Michael Tang

In characteristic zero, the Hopf algebra of quasisymmetric functions QSym is isomorphic to the shuffle algebra of compositions Sh, and isomorphisms between them can be specified via shuffle bases of QSym. We give characterizations of shuffle bases via the notions of characters and infinitesimal characters, and we establish a universal property for Sh that is analogous to the universal property of QSym as a combinatorial Hopf algebra described by Aguiar, Bergeron, and Sottile. We use these results to give general constructions of quasisymmetric power sums, a class of bases for QSym which are closely related to shuffle bases, and prove properties of some larger families of quasisymmetric power sums. (This is joint work with Ricky Liu.)