Title: P-partition power sums
|Affiliation:||University of British Columbia|
|Room/Zoom:||MC5479 or for Zoom link contact Logan Crew or Olya Mandelshtam|
The Hopf algebra of symmetric functions is spanned by several important bases, including by power sum symmetric functions, which encode the class values of the characters of the symmetric group under the Frobenius characteristic map. We introduce in this talk the basis of combinatorial power sums, naturally refining the power sum symmetric functions, for the larger Hopf algebra of quasisymmetric functions. Our construction is motivated by the theory of (weighted) P-partitions, the combinatorics of which will allow us to describe formulas for products, coproducts and classical quasisymmetric involutions, as well as give combinatorial rules for the expansion into the monomial and fundamental bases of quasisymmetric functions. Joint work with Farid Aliniaeifard and Steph van Willigenburg.