On-line, 245 pages

Dominique Foata, Guo-Niu Han

q-SERIES IN COMBINATORICS; PERMUTATION STATISTICS

• 1. The q-binomial theorem
• 2. Mahonian Statistics
• 3. The algebra of q-binomial coefficients
• 4. The q-binomial structures
• 5. The q-multinomial coefficients
• 6. The MacMahon Verfahren
• 7. A refinement of the MacMahon Verfahren
• 8. The Euler-Mahonian polynomials
• 9. The Insertion technique
• 10. The two classes of q-Eulerian polynomials
• 11. Major Index and Inversion Number
• 12. Major and Inverse Major Indices
• 13. A four-variable distribution
• 14. Symmetric Functions
• 15. The Schur Functions
• 16. The Cauchy Identity
• 17. The Combinatorial definition of the Schur Functions
• 18. The inverse ligne of route of a standard tableau
• 19. The Robinson-Schensted correspondence
• 20. Eulerian Calculus; the first extensions
• 21. Eulerian Calculus; the analytic choice
• 22. Eulerian Calculus; finite analogs of Bessel functions
• 23. Eulerian Calculus; multi-indexed polynomials
• 24. The basic and bibasic trigonometric Functions
• 25. MacMahonÕs Master Theorem revisited
• 26. The decrease value theorem
• 27. The Decrease Value Theorem; from words to permutations

• pdf