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  1. Certified source elimination for localized odd Weil formsScott SchubrEdition 2 · 2026-10-27 Public
  2. Trace-perturbed minimizers of the mixed discriminantScott SchubrEdition 2 · 2026-10-27 Public
  3. Single-copy learning of noisy stabilizers by certified filteringScott SchubrEdition 2 · 2026-10-27 Public
  4. Exponential growth of sparse Euler products and normal graded domainsScott SchubrEdition 2 · 2026-10-27 Public
  5. Phase transitions and effective curvature bounds in Fourier density modelsScott SchubrEdition 2 · 2026-10-27 Public
  6. Sharp Stability and Geometric Classification of a Vámos Quartic DeformationScott SchubrEdition 2 · 2026-10-27 Public
  7. Strong permanent inequalities for cycles and a class of single-chord supportsScott SchubrEdition 2 · 2026-10-27 Public
  8. Sharp Quadratic Smoothing for Truncated Simplex SumsScott SchubrEdition 2 · 2026-10-27 Public
  9. Sharp limitations of two permanental cofactor comparisonsScott SchubrEdition 2 · 2026-10-27 Public
  10. Three-point positivity for weighted products of Riemann theta density powersScott SchubrEdition 2 · 2026-10-27 Public
  11. Strong permanent inequalities on three chorded seven-cycle supportsScott SchubrEdition 2 · 2026-10-27 Public
  12. Coupled permanent cofactors: sharp occupation bounds and compensation geometryScott SchubrEdition 11 · 2026-10-27 Public
  13. Strong permanent inequalities for three-row bipartite supports and triangle-free supports through order sevenScott SchubrEdition 2 · 2026-10-27 Public
  14. Strong permanent contraction on four-row bipartite supports through six columnsScott SchubrEdition 2 · 2026-10-27 Public
  15. Strong permanent contraction on four-by-seven bipartite supportsScott SchubrEdition 2 · 2026-10-27 Public
  16. Finite-order positivity and growing negative inertia for averaged Riemann theta productsScott SchubrEdition 2 · 2026-10-27 Public
  17. Row-dependent bounds for strong permanent contraction on four-by-eight supportsScott SchubrEdition 2 · 2026-10-27 Public
  18. Compact capture and protected bridges on the Koras–Russell cylinderScott SchubrEdition 2 · 2026-10-27 Public
  19. Dimension-dependent holomorphic certificate degrees on zero-sum hyperplanesScott SchubrEdition 2 · 2026-10-27 Public
  20. Admissible kernel lifts with positive endpoint forms and nonreal Fourier zerosScott SchubrEdition 2 · 2026-10-27 Public
  21. Global finite-depth stability and nonreal zeros of admissible Fourier transformsScott SchubrEdition 2 · 2026-10-27 Public
  22. A Weyl Law for Rapidly Twisted Polar-Strip TubesScott SchubrEdition 2 · 2026-10-27 Public
  23. Weighted polynomial localization and theta correction inertiaScott SchubrEdition 2 · 2026-10-27 Public
  24. Weyl Laws and Angular Stability for Rapidly Twisted TubesScott SchubrEdition 2 · 2026-10-27 Public
PublicEdition 1

Closure correlations in paving and low-corank matroids

Scott Schubr

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Abstract

Sample an independent set after deleting two marked elements of a finite matroid, with probability proportional to the product of its element weights. We prove that the two events that the sampled set spans the marked elements are positively correlated for every paving matroid and for every matroid of corank at most three. In both cases the covariance numerator has nonnegative coefficients in the individual weights. The paving result follows from a monomial-preserving circuit exchange and extends to a condition on circuits through just one mark. The low-corank result uses complementary spanning sets in the dual and a coefficient inequality for two pencils of lines. Exact minor and series and parallel extension identities give further closure properties, and the proofs yield strictness criteria for positive weights. We also give a portable integer certificate for the binary rank-four consequence of earlier reported computations, including its forest-connectivity specialization.

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