A determinant of symmetric forms

✍ Scribed by K.V Menon

• Publisher: Elsevier Science
• Year: 1984
• Tongue: English
• Weight: 231 KB
• Volume: 48
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(84)90134-1

✦ Synopsis

It is proved that Z~(a+/3)>~A(a)+A ([3). This inequality is generalised for certain symmetric functions defined by Littlewood. Let O(a +/3) = r~(,~+m t, --~,-,+1,,, kt, k2 ..... ~)1.

Then we prove that D(a+/3)~>O(a)+O(/3). Here ~.1,/t2, ~-3 ..... ~ is a partition such that ~., >k,_ l >-.. >~.2>hl. o If /..I,=(~L1,/A, 2 ..... hi,S), //,l~>/d,2~>'''~/./,S is a partition of n, then in 1-2] Littlewood has defined certain symmetric functions Or.