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Asymptotic behavior of Wronskian polynomials that are factorized via \(p\)-cores and \(p\)-quotients. (English) Zbl 1451.42037

Summary: In this paper we consider Wronskian polynomials labeled by partitions that can be factorized via the combinatorial concepts of \(p\)-cores and \(p\)-quotients. We obtain the asymptotic behavior for these polynomials when the \(p\)-quotient is fixed while the size of the \(p\)-core grows to infinity. For this purpose, we associate the \(p\)-core with its characteristic vector and let all entries of this vector simultaneously tend to infinity. This result generalizes the Wronskian Hermite setting which is recovered when \(p = 2\).

MSC:

42C05 Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis
05A17 Combinatorial aspects of partitions of integers
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
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