Zeroes of Wronskians of Hermite polynomials and Young diagrams

2010/05/15 by Giovanni Felder, Felder, G., Adrian D. Hemery +3 · 2 citations
Mathematics · #26C10 #33C45 #34M35 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #FOS: Physical sciences #Mathematical Physics (math-ph) #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.1005.2695

openalex publication_date 2010/05/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a certain class of partitions, a simple qualitative relation is observed between the shape of the Young diagram and the pattern of zeroes of the Wronskian of the corresponding Hermite polynomials. In the case of two-term Wronskian W(H_n, H_n+k) we give an explicit formula for the asymptotic shape of the zero set as n → ∞. Some empirical asymptotic formulas are given for the zero sets of three and four-term Wronskians.

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