Diagonal concavity does not imply concavity for sums of elementary symmetric polynomials
Year: 2026
Type: preprint
Abstract: For positive M, let f=1+Mσ₁+σ₂+Mσ₃+σ₄ in four variables. Its fourth root is concave on the positive diagonal exactly when M≥1. It is concave on the full positive orthant exactly when M=1. Every M>1 therefore disproves Lachaume’s diagonal criterion with strictly positive coefficients.
Author: Goyal, Dev D.
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223906223