Diagonal concavity does not imply concavity for sums of elementary symmetric polynomials
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.
Authors
- Dev D. Goyal (ORCID: https://orcid.org/0009-0009-9132-744X)
Publication Details
- Journal
- Zenodo (CERN European Organization for Nuclear Research)
- Published
- 2026-10-26
- DOI
- https://doi.org/10.5281/zenodo.23679301
- Primary Topic
- Mathematical Inequalities and Applications
- Type
- preprint