Annals of Combinatorics 2 (1998) 61-83Some Combinatorial Conjectures for Jack Polynomials Michel Lassalle Ecole Polytechnique, 91128 Palaiseau Cedex, France
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. |