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  1. Strong Self-Permanent Inequalities for Complex Four-Row Bipartite SupportsScott SchubrEdition 3 · 2026-10-28 Public
  2. Sharp trace-degree certificates for rank-two permanent-derivative compensationScott SchubrEdition 2 · 2026-10-27 Public
  3. A quantitative Chollet inequality for rank-four matrices of order sevenScott SchubrEdition 2 · 2026-10-27 Public
  4. Trace-perturbed minimizers of the mixed discriminantScott SchubrEdition 2 · 2026-10-27 Public
  5. Chollet's inequality for positive semidefinite matrices of rank at most fourScott SchubrEdition 2 · 2026-10-27 Public
  6. Strong permanent inequalities for cycles and a class of single-chord supportsScott SchubrEdition 2 · 2026-10-27 Public
  7. Sharp limitations of two permanental cofactor comparisonsScott SchubrEdition 2 · 2026-10-27 Public
  8. Strong permanent inequalities on three chorded seven-cycle supportsScott SchubrEdition 2 · 2026-10-27 Public
  9. Coupled permanent cofactors: sharp occupation bounds and compensation geometryScott SchubrEdition 11 · 2026-10-27 Public
  10. Strong permanent inequalities for three-row bipartite supports and triangle-free supports through order sevenScott SchubrEdition 2 · 2026-10-27 Public
  11. Strong permanent contraction on four-row bipartite supports through six columnsScott SchubrEdition 2 · 2026-10-27 Public
  12. Strong permanent contraction on four-by-seven bipartite supportsScott SchubrEdition 2 · 2026-10-27 Public
  13. Finite-order positivity and growing negative inertia for averaged Riemann theta productsScott SchubrEdition 2 · 2026-10-27 Public
  14. Row-dependent bounds for strong permanent contraction on four-by-eight supportsScott SchubrEdition 2 · 2026-10-27 Public
  15. Sharp permanent-derivative compensation on the flat equal-spectrum conjugate-disjoint Gram stratumScott SchubrEdition 2 · 2026-10-27 Public
  16. Variance cancellation and two-direction bounds for six-row permanent derivativesScott SchubrEdition 2 · 2026-10-27 Public
  17. Real-section permanent-derivative compensation and quadratic phase controlScott SchubrEdition 2 · 2026-10-27 Public
  18. Full-phase permanent-derivative compensation under real-part spectral pinchingScott SchubrEdition 2 · 2026-10-27 Public
  19. Phase-boundary reduction and low-rank compensation for permanent derivativesScott SchubrEdition 2 · 2026-10-27 Public
  20. Asymptotically optimal bounds for permanental cofactor matricesScott SchubrEdition 2 · 2026-10-27 Public
  21. Uniform permanent-derivative compensation on the six-row conjugate-disjoint Gram locusScott SchubrEdition 2 · 2026-10-27 Public
PublicEdition 3

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

Scott Schubr ORCID

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Abstract

For every finite column count, we prove the strong self-permanent inequality for complex positive semidefinite matrices whose off-diagonal support lies in a bipartite graph with one part of size four. The conclusion bounds the permanent of the entrywise squared modulus by the permanent of the original matrix times the product of its diagonal entries. The proof removes column-dependent moment restrictions: a matching-polytope bound controls row overlaps, paired endpoint deletion gives a column-independent scalar estimate, and a large-entry transfer completes the argument. Arbitrary complex phases, missing edges and singular matrices are included. A separate extension establishes the same inequality on five-by-five bipartite supports by combining the analytic reductions with an exact tensor Bernstein certificate. We also prove a dimension-free energy criterion for the ordinary self-Chollet inequality, covering all positive semidefinite bipartite supports with one part of size at most twelve, together with further five-row regimes. The earlier three-row core and the large-entry transfer are proved within the manuscript. The finite certificate is reconstructed by a portable exact-arithmetic supplement.

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