Title: QSym and the Shuffle Compatibility of Permutation Statistics

Date: 02/25/2019

Time: 3:00 PM - 4:00 PM

Place: C517 Wells Hall

The fundamental basis of the Hopf algebra of quasisymmetric functions can be thought of in terms of shuffling permutations, however we do not distinguish between permutations that have the same descent set. We can thus think of the algebra structure of QSym as having a basis indexed by equivalence classes of permutations. This descent set, Des, is a simple example of a permutation statistic that exhibits a property called being shuffle compatible. We will show that permutation statistics that are shuffle compatible give rise to “shuffle algebras” that are quotients of QSym and then discuss some bijective proofs that certain statistics are shuffle compatible.