Maximal Degrees for Young Diagrams in the (k,l) Hook

Among the partitions λ = (λ1,λ2,…) of a largenwhich are in the (k,ℓ) hook (i.e., λk + 1 ≤ ℓ), a λ whose degreedλis maximal is approximately located. The lengths of the rows and of the columns of such λ are aboutnk + ℓ, and, similar to the ‘strip’ case (Askey and Regev,Eur. J. Combin.5(1984), 189–191), these lengths are determined by the zeroes of thek-th and of the ℓ-th Hermite polynomials.