Stanley Symmetric Functions: Episode I

Stanley Symmetric Functions are a family of symmetric functions indexed by permutations. They were originally defined to study the combinatorics of reduced words in the symmetric group. We will prove their symmetry and Schur-positivity and discuss how they are related to some of our other favorite things in symmetric function theory. We will also discuss a recent generalization of Stanley Symmetric Functions to affine permutations. Yi will keep the good times rolling with more (affine) Stanley Symmetric Functions next week.