Manuscripts and Publications
on
Macdonald Polynomials
The n! Conjecture
and
Other Amenities
Summaries of latest manuscripts (PostScript
71K)
pantpebbles.pdf
sayred.pdf
- A. M. Garsia and N. Wallach
Qsym over Sym is Free
- A. M. Garsia
Pebbles and expansions in the Polynomial ring
- A. M. Garsia
The Saga of Reduced Factorizations of Elements of the Symmetric Group
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A. M. Garsia and J. Haglund,
A Proof of the q,t-Catalan Positivity Conjecture
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A. Garsia and M. Zabrocki, Polynomiality
of the q,t-Kotska revisited
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To appear in a Volume dedicated to the
memory of G. C. Rota edited by Domenico Senato U. of Basilicata.
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math.QA/0008199
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A. M. Garsia and C. Procesi, On certain
graded Sn-modules and the q-Kostka polynomials
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Advances in Mathematics, #94 (1992)
82-138.
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N. Bergeron and A. M. Garsia, On Certain
Spaces of Harmonic Polynomials, Hypergeometric Functions on domains of
Positivity, Jack polynomials and Applications
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Contemporary Mathematics, #138 (1992)
51-86.
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A. Garsia, Orthogonality of Milne's
polynomials and raising operators
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Discrete Mathematics #99 (1992) 247-264.
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A. Garsia, Recent Progress on the
Macdonald q,t-Kostka conjecture
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Actes du 4e Colloque sur
les Series Formelles et Combinatoire Algebrique, U.Q.A.M. , Pub. L.A.C.I.M.
Montreal, (1992) 249-255.
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A. M. Garsia and M. Haiman, A graded
representation module for Macdonald's polynomials
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Proc. Natl. Acad. Sci. USA V 90 (1993)
3607-3610.
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A. Garsia and M. Haiman, Orbit Harmonics
and Graded Representations
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A. M. Garsia and M. Haiman, Factorizations
of Pieri rules for Macdonald polynomials
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Discrete Mathematics 139 (1995) 219-256.
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M. Haiman, Conjectures on the quotient
ring by diagonal invariants.
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A. Garsia and M. Haiman, A Remarkable
q,t-Catalan Sequence and q-Lagrange inversion
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A. Garsia and M. Haiman, Some bigraded
Sn-modules and the Macdonald q,t-Kostka coefficients
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Electronic Journal of Alg. Comb. V.
3 #2 (1996) pp. 561-620.
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All
versions
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A. Garsia and M. Haiman, A random
q,t-hook walk and a Sum of Pieri Coefficients
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A. M. Garsia and G. Tesler, Plethystic
Formulas for the Macdonald q,t-Kostka coefficients
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Advances in Mathematics, V. 123 #2 (1996)
pp. 144-222.
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PostScript
(630 K)
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Abstract included in above "Summaries"
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A. M. Garsia and J. Remmel, Plethystic
Formulas and positivity for q,t-Kostka Coefficients
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Mathematical Essays in Honor of Gian-Carlo
Rota, B. Sagan & R. Stanley. Ed., Progress in Mathematics V 161, Birkhauser
(1998) pp. 245-262
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Francois Bergeron and A. Garsia, Science
Fiction and Macdonald Polynomials
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Lattice Diagram Polynomials and Extended
Pieri Rules (joint with F. and N. Bergeron, M. Haiman and G. Tesler).
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Identities and conjectures for a remarkable
operator on Symmetric Polynomials (with F. Bergeron)
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Abstract included in above "Summaries"
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Explicit Plethystic Formulas for the
Macdonald q,t-Kostka Coefficients (with M. Haiman and G. Tesler)
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Multiple left regular representations
associated with alternants of the symmetric Groups , (with F. Bergeron
and G. Tesler)
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Abstract included in above "Summaries"
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G. Tesler, Isotypic Decompositions
of Lattice Determinants
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Journal of Combinatorial Theory, Series
A, to appear.
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J. Morse, Some classical expansions
for Sahi-Knop and Macdonald polynomials
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to appear in Proceedings of the 38th
Lotharingian Seminar, #38, (1996).
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Abstract included in above "Summaries"
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J. Morse, Sahi-Knop polynomials and
basic hypergeometric series
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Proceedings of Formal Power Series and
Algebraic Combinatorics, #3, 437-446 (1997).
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J. Morse, Recursions and Explicit
formulas for particular n-variable Sahi-Knop and Macdonald polynomials
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submitted to Journal of Combinatorial
Theory Series A, 16 pages, November (1997).
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Abstract included in above "Summaries"
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J. Morse, Sahi-Knop and Macdonald
polynomials Related to q-Ultraspherical functions and basic hypergeometric
series
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submitted to Discrete Mathematics, 10
pages, September (1997).
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Abstract included in above "Summaries"
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J. Morse, Determinantal Expressions
of Macdonald polynomials (with A. Lascoux and L. Lapointe).
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M. Zabrocki, On the action of the
Hall-Littlewood vertex operator
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Doctoral Thesis, UCSD (1998)
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Abstract included in above "Summaries"
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E. Reiner, Some Applications of the
Theory of Orbit Harmonics
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E. Reiner, A Proof of the n! Conjecture
for Generalized Hooks
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Journal of Comb. Theory Series A (accepted).
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E. Reiner, Variation on a Theme of
Solomon
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To be submitted for the Proceedings
of the Taormina Conference in Algebraic Combinatorics, July 1994
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Joseph Alfano, A basis for the Y2
subspace of Diagonal Harmonics
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E. Allen, A conjecture of Procesi
and the Straightening Algorithm of Rota
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Proc. Nat. Accad. V89 1992 3980-3984
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E. Allen, A conjecture of Procesi
and a new Basis for the Standard Graded Left Regular Representation of
Sn
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Advances in Math. V100 #2 1993 262-292.
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E. Allen, The Descent Monomials and
a Basis for the Diagonally Symmetric Polynomials
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Journal of Algebraic Combinatorics,
V3 1994 5-16.
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E. Allen, The Decomposition of a Bigraded
Left Regular Representation of the Diagonal Action of Sn
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Journal of Comb. Theory Series A, Series
A Vol 71, No. 1, (1995) 97-111
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E. Allen, New Bases for the Decomposition
of the Graded Left Regular Representation of the Reflection Groups of types
Bn and Dn
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Journal of Algebra, 173, (1995) 122-143.
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E. Allen, Bitableau Bases for Diagonally
Symmetric Polynomial Quotient Rings
Last Updated: August 25, 2000
First Applet (central limit theorem)