Some Combinatorial Properties of Skew Jack Symmetric Functions

Motivated by Stanley's conjecture on the multiplication of Jack symmetric functions, we prove a couple of identities showing that skew Jack symmetric functions are semi-invariant up to translation and rotation of a $\pi$ angle of the skew diagram. It follows that, in some special cases, the coe...

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Bibliographic Details
Published inThe Electronic journal of combinatorics Vol. 29; no. 2
Main Authors Bravi, Paolo, Gandini, Jacopo
Format Journal Article
LanguageEnglish
Published 06.05.2022
Online AccessGet full text
ISSN1077-8926
1077-8926
DOI10.37236/10542

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Summary:Motivated by Stanley's conjecture on the multiplication of Jack symmetric functions, we prove a couple of identities showing that skew Jack symmetric functions are semi-invariant up to translation and rotation of a $\pi$ angle of the skew diagram. It follows that, in some special cases, the coefficients of the skew Jack symmetric functions with respect to the basis of the monomial symmetric functions are polynomials with nonnegative integer coefficients.
ISSN:1077-8926
1077-8926
DOI:10.37236/10542