The Malvenuto-Reutenauer Hopf Algebra of Permutations

Table of Contents

1. Monomial Functions in terms of the Fundamental Basis.
2. Products in the Fundamental Basis.
3. Products in the Monomial Basis.
4. Antipode in the Fundamental Basis.
5. Antipode in the Monomial Basis.
6. Lie Bracket of Primitive Elements.
7. Hopf cocycle on primitive elements for smash product of decomposiiton of SSym.
8. Hopf cocycle on elements of the M-basis of QSym.