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arXiv · 2508.03568

A plethystic chain rule

Alessandro D'Andrea·Enrico Fatighenti·Claudio Onorati
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Abstract

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 $f$.

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Alessandro D'Andrea, Enrico Fatighenti, Claudio Onorati. 2026-07-18. A plethystic chain rule. https://arxiv.org/abs/2508.03568

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