Annals of Combinatorics 2 (1998) 61-83


Some Combinatorial Conjectures for Jack Polynomials

Michel Lassalle

Ecole Polytechnique, 91128 Palaiseau Cedex, France
lassalle@labri.u-bordeaux.fr

Received April 16, 1998

AMS Subject Classification: 33C50, 33C80, 22E30

Abstract. We present several combinatorial conjectures related to the expansion of Jack polynomials in terms of power sums.

Keywords: Jack polynomials, Schur functions, Pieri formula


References

1.  M. Lassalle, Une formule de Pieri pour les polynômes de Jack, C. R. Acad. Sci. Paris 309 (I) (1989) 941–944.

2.  M. Lassalle, Some combinatorial conjectures for shifted Jack polynomials, Ann. Combin., to appear.

3.  M. Lassalle, Quelques conjectures combinatoires relatives à la formule classique de Chu- Vandermonde, Adv. Appl. Math., to appear.

4.  M. Lassalle, Explicitation des polynômes de Jack, in preparation.

5.  I.G. Macdonald, Symmetric Functions and Hall Polynomials, second edition, Clarendon Press, Oxford, 1995.

6.  A. Okounkov and G. Olshanski, Shifted Jack polynomials, binomial formula and applications, Math. Res. Lett. 4 (1997) 69–78.

7.  A. Okounkov, (Shifted) Macdonald polynomials: q-integral representation and combinatorial formula, Comp. Math., to appear.

8.  R.P. Stanley, Some combinatorial properties of Jack symmetric functions, Adv. Math. 77 (1989) 76–115.


Get the LaTex | DVI | PS file of this abstract.

back