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

A. M. Garsia and J. Haglund,
A Proof of the q,tCatalan Positivity Conjecture

A. Garsia and M. Zabrocki, Polynomiality
of the q,tKotska revisited

To appear in a Volume dedicated to the
memory of G. C. Rota edited by Domenico Senato U. of Basilicata.

math.QA/0008199



A. M. Garsia and C. Procesi, On certain
graded S_{n}modules and the qKostka polynomials

Advances in Mathematics, #94 (1992)
82138.




N. Bergeron and A. M. Garsia, On Certain
Spaces of Harmonic Polynomials, Hypergeometric Functions on domains of
Positivity, Jack polynomials and Applications

Contemporary Mathematics, #138 (1992)
5186.




A. Garsia, Orthogonality of Milne's
polynomials and raising operators

Discrete Mathematics #99 (1992) 247264.




A. Garsia, Recent Progress on the
Macdonald q,tKostka conjecture

Actes du 4^{e} Colloque sur
les Series Formelles et Combinatoire Algebrique, U.Q.A.M. , Pub. L.A.C.I.M.
Montreal, (1992) 249255.




A. M. Garsia and M. Haiman, A graded
representation module for Macdonald's polynomials

Proc. Natl. Acad. Sci. USA V 90 (1993)
36073610.




A. Garsia and M. Haiman, Orbit Harmonics
and Graded Representations

A. M. Garsia and M. Haiman, Factorizations
of Pieri rules for Macdonald polynomials

Discrete Mathematics 139 (1995) 219256.




M. Haiman, Conjectures on the quotient
ring by diagonal invariants.

A. Garsia and M. Haiman, A Remarkable
q,tCatalan Sequence and qLagrange inversion

A. Garsia and M. Haiman, Some bigraded
S_{n}modules and the Macdonald q,tKostka coefficients

Electronic Journal of Alg. Comb. V.
3 #2 (1996) pp. 561620.


All
versions


A. Garsia and M. Haiman, A random
q,thook walk and a Sum of Pieri Coefficients

A. M. Garsia and G. Tesler, Plethystic
Formulas for the Macdonald q,tKostka coefficients

Advances in Mathematics, V. 123 #2 (1996)
pp. 144222.


PostScript
(630 K)

Abstract included in above "Summaries"

A. M. Garsia and J. Remmel, Plethystic
Formulas and positivity for q,tKostka Coefficients

Mathematical Essays in Honor of GianCarlo
Rota, B. Sagan & R. Stanley. Ed., Progress in Mathematics V 161, Birkhauser
(1998) pp. 245262




Francois Bergeron and A. Garsia, Science
Fiction and Macdonald Polynomials

Lattice Diagram Polynomials and Extended
Pieri Rules (joint with F. and N. Bergeron, M. Haiman and G. Tesler).

Identities and conjectures for a remarkable
operator on Symmetric Polynomials (with F. Bergeron)




Abstract included in above "Summaries"

Explicit Plethystic Formulas for the
Macdonald q,tKostka Coefficients (with M. Haiman and G. Tesler)

Multiple left regular representations
associated with alternants of the symmetric Groups , (with F. Bergeron
and G. Tesler)




Abstract included in above "Summaries"

G. Tesler, Isotypic Decompositions
of Lattice Determinants

Journal of Combinatorial Theory, Series
A, to appear.




J. Morse, Some classical expansions
for SahiKnop and Macdonald polynomials

to appear in Proceedings of the 38th
Lotharingian Seminar, #38, (1996).



Abstract included in above "Summaries"

J. Morse, SahiKnop polynomials and
basic hypergeometric series

Proceedings of Formal Power Series and
Algebraic Combinatorics, #3, 437446 (1997).




J. Morse, Recursions and Explicit
formulas for particular nvariable SahiKnop and Macdonald polynomials

submitted to Journal of Combinatorial
Theory Series A, 16 pages, November (1997).



Abstract included in above "Summaries"

J. Morse, SahiKnop and Macdonald
polynomials Related to qUltraspherical functions and basic hypergeometric
series

submitted to Discrete Mathematics, 10
pages, September (1997).



Abstract included in above "Summaries"

J. Morse, Determinantal Expressions
of Macdonald polynomials (with A. Lascoux and L. Lapointe).

M. Zabrocki, On the action of the
HallLittlewood vertex operator

Doctoral Thesis, UCSD (1998)



Abstract included in above "Summaries"

E. Reiner, Some Applications of the
Theory of Orbit Harmonics

E. Reiner, A Proof of the n! Conjecture
for Generalized Hooks

Journal of Comb. Theory Series A (accepted).




E. Reiner, Variation on a Theme of
Solomon

To be submitted for the Proceedings
of the Taormina Conference in Algebraic Combinatorics, July 1994




Joseph Alfano, A basis for the Y^{2}
subspace of Diagonal Harmonics

E. Allen, A conjecture of Procesi
and the Straightening Algorithm of Rota

Proc. Nat. Accad. V89 1992 39803984




E. Allen, A conjecture of Procesi
and a new Basis for the Standard Graded Left Regular Representation of
S_{n}

Advances in Math. V100 #2 1993 262292.




E. Allen, The Descent Monomials and
a Basis for the Diagonally Symmetric Polynomials

Journal of Algebraic Combinatorics,
V3 1994 516.




E. Allen, The Decomposition of a Bigraded
Left Regular Representation of the Diagonal Action of S_{n}

Journal of Comb. Theory Series A, Series
A Vol 71, No. 1, (1995) 97111




E. Allen, New Bases for the Decomposition
of the Graded Left Regular Representation of the Reflection Groups of types
B_{n} and D_{n}

Journal of Algebra, 173, (1995) 122143.




E. Allen, Bitableau Bases for Diagonally
Symmetric Polynomial Quotient Rings
Last Updated: August 25, 2000
First Applet (central limit theorem)