On-line, 245 pages
Dominique Foata, Guo-Niu Han
q-SERIES IN COMBINATORICS; PERMUTATION STATISTICS
Table of Contents
- 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
foata@unistra.fr, guoniu@unistra.fr
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