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Minimal matroids in dependency posets: algorithms and applications to computing irreducible decompositions of circuit varieties

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arxiv 2502.00799 v1 pith:55KMQAQD submitted 2025-02-02 math.CO math.ACmath.AG

classification math.COmath.ACmath.AG
keywords matroidsconfigurationsminimalcircuitordervarietiesalgorithmdependency
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We study point-line configurations, their minimal matroids, and their associated circuit varieties. We present an algorithm for identifying the minimal matroids of these configurations with respect to dependency order, or equivalently, the maximal matroids with respect to weak order, and use it to determine the irreducible decomposition of their corresponding circuit varieties. Our algorithm is applied to several classical configurations, including the Fano matroid, affine plane of order three, MacLane, and Pappus configurations. Additionally, we explore the connection to a conjecture by Jackson and Tanigawa, which provides a criterion for the uniqueness of the minimal matroids.

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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Algebraic Geometry of Cactus, Pascal, and Pappus Matroids

    math.CO 2025-06 conditional novelty 6.0 of 10

    For cactus, Pascal, and Pappus configurations, the matroid ideal is generated, up to radical, by circuit, Grassmann-Cayley, and liftability polynomials.

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