Motivated by Stanley’s conjecture on the multiplication of Jack symmetric func-tions, we prove a couple of identities showing that skew Jack symmetric functions are semi-invariant up to translation and rotation of a π 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.
Some combinatorial properties of skew Jack symmetric functions / Bravi, P.; Gandini, J.. - In: ELECTRONIC JOURNAL OF COMBINATORICS. - ISSN 1077-8926. - 29:2(2022). [10.37236/10542]
Some combinatorial properties of skew Jack symmetric functions
Bravi P.;
2022
Abstract
Motivated by Stanley’s conjecture on the multiplication of Jack symmetric func-tions, we prove a couple of identities showing that skew Jack symmetric functions are semi-invariant up to translation and rotation of a π 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.| File | Dimensione | Formato | |
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