Some combinatorial conjectures for Jack polynomials

descriptionPublicationkeyboard_double_arrow_right Article 01 Mar 1998 English Publisher:Springer Science and Business Media LLCJournal:Annals of Combinatorics, volume 2, pages 61-83 (issn: 0218-0006, eissn: 0219-3094,

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Authors: Lassalle, Michel;

doi: 10.1007/bf01626029

Some combinatorial conjectures for Jack polynomials

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Abstract

After an exposition of Jack polynomials, shifted symmetric polynomials and a generalization of Stirling numbers of the kirst kind, this paper presents conjectures concerning a generalization of the Pieri formula and the expansion of Jack polynomials in terms of power sums. These conjectures are well supported by numerical evidence, which is contained in the paper in form of several tables. Specialization leads to new conjectures concerning Schur functions.

Related Organizations

École Polytechnique
France

Keywords

Symmetric functions and generalizations, Pieri formula, Jack polynomials, Combinatorial aspects of groups and algebras, Schur functions

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