Duff Baker-Jarvis, Wake Forest University, QSym and the Shuffle Compatibility of Permutation Statistics
The fundamental basis of the Hopf algebra of quasisymmetric functions, QSym, can be thought of in terms of shuffling permutations. We can think of QSym as having a basis indexed by equivalence classes of permutations, where we identify permutations with the same descent set. This descent set, Des, is a simple example of a permutation…