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  1. Positive Operator Cocycles in Shrinking CorridorsScott SchubrEdition 2 · 2026-10-31 Public
  2. Coherence thresholds for optimal-rate stabilizer purity testingScott SchubrEdition 2 · 2026-10-31 Public
  3. Spectral escape for interacting and coalescing signed potential formsScott SchubrEdition 5 · 2026-10-30 Public
  4. Large negative subspaces for positive Euler deformationsScott SchubrEdition 3 · 2026-10-30 Public
  5. Fourier computation of empirical diffusion metricsScott SchubrEdition 2 · 2026-10-30 Public
  6. Purity frontiers and optimal copy complexity for qutrit stabilizer measurementsScott SchubrEdition 2 · 2026-10-30 Public
  7. Polynomial cores and inertia under Carleman moment boundsScott SchubrEdition 3 · 2026-10-30 Public
  8. Collision-uniform kernel asymptotics for Báez–Duarte zero packetsScott SchubrEdition 4 · 2026-10-30 Public
  9. Mixing-weight entropy concavity near the Gaussian below one-half signalScott SchubrEdition 3 · 2026-10-30 Public
  10. Covariance-Spectrum Certificates for Homogeneous Stable Count LawsScott SchubrEdition 8 · 2026-10-30 Public
  11. Relative tail payment and spectral enclosuresScott SchubrEdition 1 · 2026-10-29 Public
  12. Joint inclusion bounds for random greedy matroid basesScott SchubrEdition 1 · 2026-10-29 Public
  13. Divisor tests and coefficient transfers for sextic character momentsScott SchubrEdition 1 · 2026-10-28 Public
  14. Strong Self-Permanent Inequalities for Complex Four-Row Bipartite SupportsScott SchubrEdition 3 · 2026-10-28 Public
  15. Signed Frequency Certificates and Constraint Costs for Odd Weil FormsScott SchubrEdition 1 · 2026-10-27 Public
  16. Frequency-Source Resolvent Limits and Positive-Receiver InstabilityScott SchubrEdition 1 · 2026-10-27 Public
  17. Source-Resolved Resolvent Growth under Reciprocal-Theta ConfinementScott SchubrEdition 1 · 2026-10-27 Public
  18. Distributional traces and central moment tests for Vámos quarticsScott SchubrEdition 1 · 2026-10-27 Public
  19. Exact-rank quadratic correlation: a phase-compatible Clique reductionScott SchubrEdition 1 · 2026-10-27 Public
  20. Certified resolvent detection of the third Weyl-blind twisting harmonicScott SchubrEdition 2 · 2026-10-27 Public
  21. Degree-eight positivity and polynomial obstructions for monotone Riemann theta averagesScott SchubrEdition 7 · 2026-10-27 Public
  22. Independent Squares and Average-Radius Obstructions for Linear CodesScott SchubrEdition 2 · 2026-10-27 Public
  23. An explicit quintic obstruction for a fixed-center Riemann theta productScott SchubrEdition 2 · 2026-10-27 Public
  24. A rational reconstruction of a quintic obstruction for a fixed-center Riemann theta productScott 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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