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 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.

Bravi, P., Gandini, J. (2022). Some Combinatorial Properties of Skew Jack Symmetric Functions. ELECTRONIC JOURNAL OF COMBINATORICS, 29(2), 1-20 [10.37236/10542].

Some Combinatorial Properties of Skew Jack Symmetric Functions

Gandini, Jacopo
2022

Abstract

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 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.
2022
Bravi, P., Gandini, J. (2022). Some Combinatorial Properties of Skew Jack Symmetric Functions. ELECTRONIC JOURNAL OF COMBINATORICS, 29(2), 1-20 [10.37236/10542].
Bravi, Paolo; Gandini, Jacopo
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/885055
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