A positivity conjecture on the structure constants of shifted Jack functions

2019/12/11 by Per Alexandersson, Valentin Féray, Alexandersson, Per +1
Mathematics · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.1912.05203

openalex publication_date 2019/12/11 · openalex created_date 2024/08/07 · openalex updated_date 2026/08/03

Abstract

We consider Jack polynomials J_λ and their shifted analogue J^#_λ. In 1989, Stanley conjectured that ⟨ J_μJ_ν, J_λ⟩ is a polynomial with nonnegative coefficients in the parameter α. In this note, we extend this conjecture to the case of shifted Jack polynomials.

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