Invariant algebras and major indices for classical Weyl groups

Proceedings of the London Mathematical Society

Volumn 88, Issue 3, 2004, Pages 603-631

  Biagioli, Riccardo ^a   Caselli, Fabrizio ^b  

^a UNIVERSITÉ DU QUÉBEC À MONTRÉAL   (Canada)

^b UNIVERSITÉ LYON 1   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 2342494179     PISSN: 00246115     EISSN: None     Source Type: Journal    
DOI: 10.1112/S0024611503014552     Document Type: Conference Paper

References (21)

1. R. M. ADIN and Y. ROICHMAN, 'The flag major index and group actions on polynomial rings', European J. Combin. 22 (2001) 431-446.
2. R. M. ADIN, F. BRENTI and Y. ROICHMAN, 'Descent numbers and major indices for the hyperoctahedral group', Adv. in Appl. Math. 27 (2001) 210-224.
3. R. M. ADIN, F. BRENTI and Y. ROICHMAN, 'Descent representations and multivariate statistics', Trans. Amer. Math. Soc. to appear.
4. R. BIAGIOLI, 'Major and descent statistics for the even-signed permutation group', Adv. in Appl. Math. 31 (2003) 163-179.
5. R. BIAGIOLI and F. CASELLI, 'A monomial basis for the coinvariant algebra of type D', J. Algebra, to appear.
6. F. BRENTI, 'q-Eulerian polynomials arising from Coxeter groups', European J. Combin. 15 (1994) 417-441.
7. L. CARLITZ, 'A combinatorial property of q-Eulerian numbers', Amer. Math. Monthly 82 (1975) 51-54.
8. R. J. CLARKE and D. FOATA, 'Eulerian calculus. I. Univariable statistics', European J. Combin. 15 (1994) 345-362.
9. R. J. CLARKE and D. FOATA, 'Eulerian calculus. II. An extension of Han's fundamental transformation', European J. Combin. 16 (1995) 221-252.
10. R. J. CLARKE and D. FOATA, 'Eulerian calculus. III. The ubiquitous Cauchy formula', European J. Combin. 16 (1995) 329-355.
11. D. FOATA, 'On the Netto inversion number of a sequence', Proc. Amer. Math. Soc. 19 (1968) 236-240.
12. D. FOATA, 'Distributions eulériennes et mahoniennes sur le groupe des permutations', Higher combinatorics, NATO Advanced Study Institute, Berlin, 1976 (ed. M. Aigner), NATO Science Series C 31 (D. Reidel, Amsterdam, 1977) 27-49.
13. A. GARSIA, 'On the "maj" and "inv" q-analogues of Eulerian polynomials', Linear and Multilinear Algebra 8 (1979/80) 21-34.
14. A. GARSIA and I. GESSEL, 'Permutation statistics and partitions', Adv. Math. 31 (1979) 288-305.
15. A. GARSIA and D. STANTON, 'Group actions of Stanley-Reisner rings and invariants of permutation groups', Adv. Math. 51 (1984) 107-201.
16. I. GESSEL, 'Generating functions and enumeration of sequences', PhD Thesis, M.I.T., 1977.
17. B. GORDON, 'Two theorems on multipartite partitions', J. London Math. Soc. 38 (1963) 459-464.
18. J. E. HUMPHREYS, Reflection groups and Coxeter groups, Cambridge Studies in Advanced Mathematics 29 (Cambridge University Press, 1990).
19. V. REINER, 'Signed permutation statistics', European J. Combin. 14 (1993) 553-567.
20. P. A. MACMAHON, Combinatory analysis, vol. 1 (Cambridge University Press, London, 1915).
21. E. STEINGRIMSSON, 'Permutation statistics of indexed permutations', European J. Combin. 15 (1994) 187-205.