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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| Published in | The Electronic journal of combinatorics Vol. 29; no. 2 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
06.05.2022
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| Online Access | Get full text |
| ISSN | 1077-8926 1077-8926 |
| DOI | 10.37236/10542 |
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| 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 $\pi$ 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. |
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| AbstractList | 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. |
| Author | Gandini, Jacopo Bravi, Paolo |
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| Snippet | Motivated by Stanley's conjecture on the multiplication of Jack symmetric functions, we prove a couple of identities showing that skew Jack symmetric functions... |
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| Title | Some Combinatorial Properties of Skew Jack Symmetric Functions |
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