Asymptotic behavior of Wronskian polynomials that are factorized via $p$-cores and $p$-quotients

Abstract

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 $p=2$.

arXiv comment22 pages, 15 figures

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Cited by in corpus (2)

• Rational Solutions of the Fifth Painlevé Equation. Generalised Laguerre Polynomials
• The Expansion of Wronskian Hermite Polynomials in the Hermite Basis