Catalan paths and quasi-symmetric functions

Proceedings of the American Mathematical Society

Volumn 131, Issue 4, 2003, Pages 1053-1062

  Aval, J C ^a   Bergeron, N ^b  

^a UNIVERSITÉ BORDEAUX 1   (France)

^b YORK UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037385193     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9939-02-06634-0     Document Type: Conference Paper

References (18)

1. E. ARTIN, Galois Theory, Notre Dame Mathematical Lecture 2 (1944), Notre Dame, IN. MR 5:225c; reprint MR 98k:12001, MR 42:234
2. n, to appear (Math. co 10202071).
3. J.-C. AVAL, F. BERGERON, N. BERGERON AND A. GARSIA, Ideals of Quasi-symmetric polynomials and related varieties, in preparation.
4. F. BERGERON, N. BERGERON, A. GARSIA, M. HAIMAN AND G. TESLER, Lattice Diagram Polynomials and Extended Pieri Rules, Adv. Math. 142 (1999), 244-334. MR 2000h:05231
5. F. BERGERON, A. GARSIA AND G. TESLER, Multiple Left Regular Representations Generated by Alternants, J. of Comb. Th., Series A 91, 1-2 (2000), 49-83. MR 2002c:05158
6. N. BERGERON, S. MYKYTIUK, F. SOTTILE, AND S. VAN WILLIGENBURG, Pieri Operations on Posets, J. of Comb. Theory, Series A 91 (2000), 84-110.
7. C. DE CONCINI AND C. PROCESI, Symmetric functions, conjugacy classes and the flag variety, Invent. Math. 64 (1981), 203-230. MR 82m:14030
8. D. Cox, J. LITTLE AND D. O'SHEA, Ideals, Varieties, and Algorithms, Springer-Verlag, New-York, 1992. MR 93j:13031; second edition MR 97h:13024
9. A. M. GARSIA AND M. HAIMAN, A graded representation model for Macdonald's polynomials, Proc. Nat. Acad. Sci. U.S.A. 90 (1993), no. 8, 3607-3610. MR 94b:05206
10. I. GELFAND, D. KROB, A. LASCOUX, B. LECLERC, V. RETAKH, AND J.-Y. THIBON, Noncommutative symmetric functions, Adv. in Math. 112 (1995), 218-348. MR 96e:05175
11. I. GESSEL, Multipartite P-partitions and products of skew Schur functions, in Combinatorics and Algebra (Boulder, Colo., 1983), C. Greene, ed., vol. 34 of Contemp. Math., AMS, 1984, pp. 289-317. MR 86k:05007
12. M. HAIMAN, Hilbert schemes, polygraphs, and the Macdonald positivity conjecture, J. Amer. Math. Soc. 14 (2001), 941-1006. MR 2002c:14008
13. F. HIVERT, Hecke algebras, difference operators, and quasi-symmetric functions, Adv. Math. 155 (2000), 181-238, CMP 2001:04
14. I. MACDONALD, Symmetric Functions and Hall Polynomials, Oxford Univ. Press, 1995, second edition. MR 96h:05207
15. C. MALVENUTO AND C. REUTENAUER, Duality between quasi-symmetric functions and the Solomon descent algebra, Journal of Algebra 177 (1995), 967-982. MR 97d:05277
16. R. STANLEY, Enumerative Combinatorics, Vol. 1, Wadsworth and Brooks/Cole, 1986. MR 87j:05003; corr. reprint MR 98a:05001
17. R. STANLEY, Enumerative Combinatorics Vol. 2, no. 62 in Cambridge Studies in Advanced Mathematics, Cambridge University Press, 1999. Appendix 1 by Sergey Fomin. MR 2000k:05026
18. R. STEINBERG, Differential equations invariant under finite reflection groups, Trans. Amer. Math. Soc. 112 (1964), 392-400. MR 29:4807