Two Generalizations of Muirhead's Theorem,
Abstract
Muirhead's theorem states that M(u, x) > or = M(u, y) whenever x majorizes y, u is a positive vector, and M(u, x) is defined to be the summation (pi belongs to S sub n) of (u sup x1, sub pi 1)...(u sup xn, sub pi n), where (S sub n) is the group of all permutations pi of (1, 2,...,n). In the note, Muirhead's theorem is generalized by replacing (u sup z, sub 1) by a function pi(i, z) which is log convex in z. The generalization of Muirhead's theorem to the continuous case by Ryff (1967) in the Pacific Journal of Mathematics is likewise generalized. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 1972
- Accession Number
- AD0771602
Entities
People
- Frank Proschan
- Jayaram Sethuraman
Organizations
- Florida State University