The diagonal derivative of a skew Schur polynomial

2024/02/22 by Darij Grinberg, Grinberg, Darij, Nazar Korniichuk +5 · 1 citation
Mathematics · #05E05 #11P81 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.2402.14217

openalex publication_date 2024/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a formula for the image of a skew Schur polynomial s_λ/μ( x₁, x₂, …, x_N) under the differential operator ∇:= \dfrac∂∂ x₁ +\dfrac∂∂ x₂+⋯+\dfrac∂∂ x_N. This generalizes a formula of Weigandt for ∇( s_λ) .

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