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August 10, 2026Open Access

Regular-Closed Flats of Matroids: Cocircuit Reconstruction, Reconstruction Defect, and Finite Obstruction Hierarchies

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Authors

PLPhilip LilienUniversity Foundation

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Implication

Demonstrates cocircuit reconstruction and its properties in matroids, suggesting new structural insights.

Key Points

  • The paper aims to explore the structure and properties of regular-closed flats in matroids, particularly focusing on cocircuit reconstruction.
  • Introduced the concepts of regular closure and cocircuit reconstruction in matroid theory.
  • Analyzed the rank defect and defined a connectivity interpretation for flats within matroids.
  • Established the minor monotonicity and relationships between excluded minors and coindependent flats.
  • Defined a new parameter for measuring maximum rank avoidance in coindependent flats, Δ(M), showing it is minor-monotone and additive under direct sums.
  • Characterized excluded minors for specific classes, indicating a rigidity in structure at each level.
  • Demonstrated connections between regular closure, dual cyclic interiors, and cocircuit structures in matroids.

Cite This Study

Philip Lilien (2026) studied this question.

synapsesocial.com/papers/6a797d299c20a9bbd31845d7https://doi.org/10.5281/zenodo.21853488
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