Inequalities and real analysis

Results in Inequalities and real analysis

• Diagonal concavity does not imply concavity for sums of elementary symmetric polynomials

  DisprovedLachaume's diagonal concavity conjecture for sums of elementary symmetric polynomials

  Mathematics · Inequalities and real analysis · shared Lean library

  For f = 1 + Mσ₁ + σ₂ + Mσ₃ + σ₄ in four variables with M > 0, f^(1/4) is concave on the positive diagonal exactly when M ≥ 1 and on the whole positive orthant exactly when M = 1, so every M > 1 is a counterexample.

  Manuscript: Diagonal concavity does not imply concavity for sums of elementary symmetric polynomials · Lean proof: Diagonal concavity does not imply concavity for sums of elementary symmetric polynomials · Verification: Diagonal concavity does not imply concavity for sums of elementary symmetric polynomials