Algebra and Combinatorics Seminar

Date: September 18, 2020

Time: 3:00PM - 4:00PM

Location: Zoom

Speaker: Jacob White, UT Rio Grande Valley

Title: Combinatorial Hopf monoids and flag f-vectors

Abstract: A combinatorial Hopf monoid in species provides an algebraic framework for understanding many polynomial and quasisymmetric function invariants in combinatorics. In this talk, we will discuss the problem of determining when the quasisymmetric functions associated to a combinatorial Hopf monoid are related to the flag f-vector of a family of relative simplicial complexes. We also discuss inequalities we obtain for the quasisymmetric functions in this situation, and describe some new examples of quasisymmetric functions, and combinatorial Hopf monoids. If there is time, we will also discuss F-positivity.