The V/L recursion for Macdonald's 7th Variation Schur polynomials
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917552226041856 |
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| author | Grinberg, Darij |
| author_facet | Grinberg, Darij |
| contents | We generalize and prove the recursive relation \[ S_λ(V) = \sum_{L\subseteq V\text{ line}} S_λ(V \mathbin{/\mkern-5mu/} L) \] conjectured by I. G. Macdonald for his "7th variation" of the Schur functions. This variation is a family of polynomials over a finite field that mimic the (straight and skew) Schur polynomials using powers of the Frobenius. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_26775 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The V/L recursion for Macdonald's 7th Variation Schur polynomials Grinberg, Darij Combinatorics Number Theory Rings and Algebras 05E05, 11T06 We generalize and prove the recursive relation \[ S_λ(V) = \sum_{L\subseteq V\text{ line}} S_λ(V \mathbin{/\mkern-5mu/} L) \] conjectured by I. G. Macdonald for his "7th variation" of the Schur functions. This variation is a family of polynomials over a finite field that mimic the (straight and skew) Schur polynomials using powers of the Frobenius. |
| title | The V/L recursion for Macdonald's 7th Variation Schur polynomials |
| topic | Combinatorics Number Theory Rings and Algebras 05E05, 11T06 |
| url | https://arxiv.org/abs/2605.26775 |