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On the toric ideal of a matroid

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2014

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Lasoń, Michał

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https://doi.org/10.1016/j.aim.2014.03.004
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http://arxiv.org/abs/1302.5236v3

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Advances in Mathematics. Elsevier. 2014, 259, pp. 1-12. ISSN 0001-8708. eISSN 1090-2082. Available under: doi: 10.1016/j.aim.2014.03.004

Zusammenfassung

Describing minimal generating set of a toric ideal is a well-studied and difficult problem. In 1980 White conjectured that the toric ideal associated to a matroid is equal to the ideal generated by quadratic binomials corresponding to symmetric exchanges.

We prove White's conjecture up to saturation, that is that the saturations of both ideals are equal. In the language of algebraic geometry this means that both ideals define the same projective scheme. Additionally we prove the full conjecture for strongly base orderable matroids.

Zusammenfassung in einer weiteren Sprache

Fachgebiet (DDC)
510 Mathematik

Schlagwörter

Matroid, Toric ideal, Base exchange, Strongly base orderable matroid

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ISO 690LASOŃ, Michał, Mateusz MICHALEK, 2014. On the toric ideal of a matroid. In: Advances in Mathematics. Elsevier. 2014, 259, pp. 1-12. ISSN 0001-8708. eISSN 1090-2082. Available under: doi: 10.1016/j.aim.2014.03.004
BibTex
@article{Lason2014toric-52452,
  year={2014},
  doi={10.1016/j.aim.2014.03.004},
  title={On the toric ideal of a matroid},
  volume={259},
  issn={0001-8708},
  journal={Advances in Mathematics},
  pages={1--12},
  author={Lasoń, Michał and Michalek, Mateusz}
}
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