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July 26, 2026Journal of the London Mathematical SocietyOpen Access

Fine multidegrees, universal Gröbner bases, and matrix Schubert varieties

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Authors

DHDaoji HuangMLMatt Larson

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Overview

Randomized trial establishes criteria for universal Gröbner bases in matrix Schubert varieties, suggesting new proofs exist.

Key Points

  • To establish a criterion for polynomials to form a universal Gröbner basis and to compute fine Schubert polynomials of matrix Schubert varieties.
  • Introduced a criterion based on multidegree for polynomials being a universal Gröbner basis.
  • Computed fine Schubert polynomials for specific permutations with 0 or 1 coefficients.
  • Presented results on the ideal of the matrix Schubert variety from these polynomials.
  • Provided a clear criterion for identifying universal Gröbner bases.
  • Derived fine Schubert polynomials for various permutations in terms of their coefficients.
  • Established a universal Gröbner basis for the ideal of the matrix Schubert variety influenced by computed polynomials.

Cite This Study

Huang et al. (2026) studied this question.

synapsesocial.com/papers/6a65a890d3aea3239cd78ec2https://doi.org/10.1112/jlms.70647
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