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| Format: | Preprint |
| Publié: |
2026
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| Accès en ligne: | https://arxiv.org/abs/2605.10608 |
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| _version_ | 1866913112675844096 |
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| author | Mickler, Ryan |
| author_facet | Mickler, Ryan |
| contents | We argue that Jack Littlewood-Richardson coefficients $g_{μν}^λ(α)$ are specialisations of certain novel polynomials. For the triple of partitions $(μ,ν,λ)=(21,21,321)$, we prove the corresponding polynomial is invariant under $S_6 \times \mathbb{Z}_2$, which is identified as the automorphism group of the Johnson graph $J(6,3)$. We conjecture that these polynomials exhibit a factorization property on certain hyperplanes, which is a consequence of compatibility relations between polynomials associated to adjacent triples in the Young graph. As a consequence of this, we conjecture that the difference of adjacent Jack Littlewood-Richardson coefficients is divisible by the shared hook length. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_10608 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Hidden Structure of Jack Littlewood-Richardson Coefficients Mickler, Ryan Combinatorics Rings and Algebras 05E05 We argue that Jack Littlewood-Richardson coefficients $g_{μν}^λ(α)$ are specialisations of certain novel polynomials. For the triple of partitions $(μ,ν,λ)=(21,21,321)$, we prove the corresponding polynomial is invariant under $S_6 \times \mathbb{Z}_2$, which is identified as the automorphism group of the Johnson graph $J(6,3)$. We conjecture that these polynomials exhibit a factorization property on certain hyperplanes, which is a consequence of compatibility relations between polynomials associated to adjacent triples in the Young graph. As a consequence of this, we conjecture that the difference of adjacent Jack Littlewood-Richardson coefficients is divisible by the shared hook length. |
| title | Hidden Structure of Jack Littlewood-Richardson Coefficients |
| topic | Combinatorics Rings and Algebras 05E05 |
| url | https://arxiv.org/abs/2605.10608 |