A plethystic chain rule
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918156953452544 |
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| author | D'Andrea, Alessandro Fatighenti, Enrico Onorati, Claudio |
| author_facet | D'Andrea, Alessandro Fatighenti, Enrico Onorati, Claudio |
| contents | We consider a derivation $\mathsf{D}$ on the ring $Λ$ of symmetric functions and investigate its combinatorial, algebraic and geometric properties. More precisely, we show that $\mathsf{D}$ restricts to a quasi-isometry, with respect to the Hall product, on the graded component of $Λ$ of each positive degree and provide a chain-rule formula with respect to the plethysm operation. Furthermore, we relate the geometry of the Schur functions supporting $\mathsf{D}(f)$, where $f\in Λ$ is an homogeneous symmetric function, to that of $f$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_03568 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A plethystic chain rule D'Andrea, Alessandro Fatighenti, Enrico Onorati, Claudio Combinatorics Algebraic Geometry We consider a derivation $\mathsf{D}$ on the ring $Λ$ of symmetric functions and investigate its combinatorial, algebraic and geometric properties. More precisely, we show that $\mathsf{D}$ restricts to a quasi-isometry, with respect to the Hall product, on the graded component of $Λ$ of each positive degree and provide a chain-rule formula with respect to the plethysm operation. Furthermore, we relate the geometry of the Schur functions supporting $\mathsf{D}(f)$, where $f\in Λ$ is an homogeneous symmetric function, to that of $f$. |
| title | A plethystic chain rule |
| topic | Combinatorics Algebraic Geometry |
| url | https://arxiv.org/abs/2508.03568 |