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

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
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preprint

Real positive-definite counterexamples to extended q-permanent monotonicity

Dev D. Goyal
Zenodo (CERN European Organization for Nuclear Research)
Mathematical Inequalities and Applications
preprint

Real positive-definite counterexamples to extended q-permanent monotonicity

Dev D. Goyal
preprint en

Abstract

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.

Zenodo (CERN European Organization for Nuclear Research)
Mathematical Inequalities and Applications
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Real positive-definite counterexamples to extended q-permanent monotonicity — Dev D. Goyal · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS