Plethystic formulas for Macdonald q, t-Kostka coefficients

Advances in Mathematics

Volumn 123, Issue 2, 1996, Pages 144-222

  Garsia, A M ^a   Tesler, G ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030579342     PISSN: 00018708     EISSN: None     Source Type: Journal    
DOI: 10.1006/aima.1996.0071     Document Type: Article

References (15)

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2. 2. A. Garsia, Orthogonality of Milne's polynomials and raising operators, Discrete Math. 99 (1992), 247-264.
3. 3. A. M. Garsia and M. Haiman, A graded representation module for Macdonald's polynomials, Proc. Natl. Acad. Sci. USA V 90 (1993), 3607-3610.
4. 4. A. M. Garsia and M. Haiman, Factorizations of Pieri rules for Macdonald polynomials, Discrete Math. 139 (1995), 219-256.
5. 5. A. M. Garsia and M. Haiman, "Orbit Harmonics and Graded Representations" (research monograph to appear as part of the collection published by the Lab. de Comb. et Informatique Mathématique, edited by S. Brlek, U. du Québec à Montréal).
6. 6. A. Garsia and M. Haiman, A Remarkable q, t-Catalan Sequence and q-Lagrange inversion, J. Algebraic Combin. 5, No. 3 (1996), 191-244.
7. n-modules and the Macdonald q, t-Kostka coefficients, Electronic J. Algebraic Combin., Foata Festschrift, Paper R24, (web site http://ejc.math.gatech.edu:8080/Journal/journalhome.html).
8. 8. A. Garsia and M. Haiman, A random q, t-hook walk and a Sum of Pieri coefficients, submitted for publication.
9. n-modules and the q-Kostka polynomials, Adv. Math. 94 (1992), 82-138.
10. 10. A. M. Garsia and J. Remmel, Plethystic formulas and positivity of the Macdonald q, t-Kostka coefficients, in preparation.
11. 11. C. Greene, A. Nijenhuis, and H. Wilf, A probabilistic proof of a formula for the number of Young tableaux of a given shape, Adv. Math. 31 (1979), 104-109.
12. 12. C. Greene, A. Nijenhuis, and H. Wilf, Another probabilistic method in the theory of Young tableaux, J. Combin. Theory Ser. A 37 (1984), 127-135.
13. e Séminaire Lotharingien, Publ. I.R.M.A. Strasbourg, (1988) 131-171.
14. 14. I. G. Macdonald, "Symmetric Functions and Hall Polynomials," 2nd ed., Clarendon Press, Oxford, 1995.
15. 15. R. Stanley, "Enumerative Combinatorics," Vol. 1, Wadsworth & Brooks/Cole, Belmont, CA, (1986).