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  1. Self-concordance and allocation for spatial power sumsScott SchubrEdition 3 · 2026-11-01 Public
  2. Sharp all-times heat-content comparison and concentration on compact metric graphsScott SchubrEdition 3 · 2026-11-01 Public
  3. Energy-Filtered Dynamical Localization in Constructive Dirichlet TowersScott SchubrEdition 3 · 2026-11-01 Public
  4. Degree-dependent minimax laws for Gaussian factorial momentsScott SchubrEdition 2 · 2026-11-01 Public
  5. A sharp lower bound for adjacent-edge correlations in random subtreesScott SchubrEdition 4 · 2026-11-01 Public
  6. Sharp transport identification with unknown Gaussian covarianceScott SchubrEdition 3 · 2026-11-01 Public
  7. Statistical inference for empirical heat-kernel Sinkhorn metricsScott SchubrEdition 5 · 2026-11-01 Public
  8. First-Hit Stopping and Bias-Corrected Score Inference in Dimension ThreeScott SchubrEdition 5 · 2026-11-01 Public
  9. Sharp Wasserstein Stability for Gaussian Deconvolution of Log-Concave LawsScott SchubrEdition 4 · 2026-11-01 Public
  10. Exact low-brightness minimax risk for quartic Gaussian energyScott SchubrEdition 1 · 2026-11-01 Public
  11. Sharp estimation costs for thermal Gaussian energies with known backgroundScott SchubrEdition 1 · 2026-11-01 Public
  12. Sharp calibration costs for high-order thermal Gaussian energiesScott SchubrEdition 1 · 2026-11-01 Public
  13. A sharp flatness transition for critical heat traces in twisted tubesScott SchubrEdition 1 · 2026-11-01 Public
  14. Prescribed-Gradient Coefficient Stability for Lorentzian PolynomialsScott SchubrEdition 1 · 2026-11-01 Public
  15. Closure correlations in paving and low-corank matroidsScott SchubrEdition 1 · 2026-11-01 Public
  16. Polynomial Recovery and Masking under Weak Exponential TailsScott SchubrEdition 4 · 2026-11-01 Public
  17. Polynomial inertia of signed measures with negative intervalsScott SchubrEdition 3 · 2026-11-01 Public
  18. Holomorphic certification on real subspacesScott SchubrEdition 3 · 2026-11-01 Public
  19. Arithmetic cutoff bounds and sharp tail capacity for local Nyman–Beurling certificatesScott SchubrEdition 5 · 2026-11-01 Public
  20. Optimal unbiased Gaussian quantum estimation and the cost of unknown squeezingScott SchubrEdition 1 · 2026-11-01 Public
  21. Optimal unbiased estimation of polynomial energies in thermal Gaussian statesScott SchubrEdition 3 · 2026-10-31 Public
  22. Unrestricted Half-Power Obstruction and Polynomial Certificates for the Vámos QuarticScott SchubrEdition 5 · 2026-10-31 Public
  23. Dimension thresholds for log-concavity of normalized mixed momentsScott SchubrEdition 3 · 2026-10-31 Public
  24. Uniform Resolvent Asymptotics for Growing Theta-Null Source FamiliesScott SchubrEdition 2 · 2026-10-31 Public
PublicEdition 3

Strong Self-Permanent Inequalities for Complex Four-Row Bipartite Supports

Scott Schubr ORCID

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Abstract

The paper proves a strong self-conjugate permanent inequality for every complex positive semidefinite matrix whose off-diagonal support is bipartite with one part of size at most four. The permanent of its entrywise squared modulus is bounded by its permanent times the product of its diagonal entries. The other part has arbitrary finite size, so the result permits unbounded matrix order and arbitrary complex cycle phases. The proof combines a matching-polytope overlap bound with a column-independent endpoint argument and a large-entry reduction. A five-by-five extension, proved by an exact polynomial certificate, gives the same strong inequality for every bipartite support through total order ten. A separate total-energy estimate gives the ordinary self-Chollet inequality on every positive semidefinite bipartite support with one part of size at most twelve. Complete analytic reductions and portable exact verification are supplied.

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