New concavity and convexity results for symmetric polynomials and their ratios

  title={New concavity and convexity results for symmetric polynomials and their ratios},
  author={Suvrit Sra},
  journal={Linear and Multilinear Algebra},
  pages={1031 - 1038}
  • S. Sra
  • Published 27 March 2018
  • Mathematics
  • Linear and Multilinear Algebra
ABSTRACT We prove ‘power’ generalizations of Marcus–Lopes style (including McLeod and Bullen) concavity inequalities for elementary symmetric polynomials, and similar generalizations to convexity inequalities of McLeod and Baston for complete homogeneous symmetric polynomials. We also present additional concavity results for elementary symmetric polynomials, of which the main result is a concavity theorem that yields a well-known log-convexity 1972 result of Muir for positive definite matrices… 

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if o>>2, c, a have common factor, .". only possible value of to is 2. = 2m, c -a = 2n and c — m + n, a = m-n. And 6 = c a? = imn .-. ran is an exact square, .-. m, n are both exact squares or have a