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

✍ Scribed by A Regev

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 102 KB
• Volume: 19
• Category: Article
• ISSN: 0195-6698
• DOI: 10.1006/eujc.1997.0200

✦ Synopsis

Among the partitions λ = (λ 1 , λ 2 , . . .) of a large n which are in the (k, ) hook (i.e., λ k+1 ≤ ), a λ whose degree d λ is maximal is approximately located. The lengths of the rows and of the columns of such λ are about n k+ , and, similar to the 'strip' case (Askey and Regev, Eur. J. Combin. 5 (1984), 189-191) , these lengths are determined by the zeroes of the k-th and of the -th Hermite polynomials.