Minimal set of class-sums characterizing the ordinary irreducible representations of the symmetric group, and the Tarry-Escott problem

✍ Scribed by Jacob Katriel

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 276 KB
• Volume: 173
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/s0012-365x(96)00099-4

✦ Synopsis

The shape of a Young diagram Y (I Y[ = n) can be specified in terms of the set of symmetric power sums over its contents, at = ~(i,j)~r(/"-i)t; ~ = 1,2 .... , n. It is remarkable that the set of power sums try, a2 .... , ak is sufficient to characterize the Young diagrams possessing up to n(k) boxes, where n(k) is considerably larger than k. Numerical evidence for k~<5 is roughly consistent with n(k) 4 2k 4(3 ) . The lower bound n(k) > k + max(2, vfk) has been derived by examination of some properties of Young diagrams with a large number of rows, and the upper bound n(k) < 22k+l has been established using a variant of the Tarry-Escort problem.