Real positive-definite counterexamples to extended q-permanent monotonicity
For every real parameter q>1, a real symmetric positive-definite matrix has a negative q-permanent derivative at q. An explicit matrix of order five decreases from q=14 to q=15. Correlation matrices with no zero entries and integer-entry examples are also obtained. The dimension can depend on q. The real-symmetric question on [−1,1] remains outside the result.
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.23679242
- Primary Topic
- Mathematical Inequalities and Applications
- Type
- preprint