On the toric ideals of matroids of a fixed rank

• Michał Lason ^[1]
  1. [1] Institute of Mathematics

     Institute of Mathematics

     Warszawa, Polonia

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 27, Nº. 2, 2021
• Idioma: inglés
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• Resumen

  • In 1980 White conjectured that every element of the toric ideal of a matroid is generated by quadratic binomials corresponding to symmetric exchanges. We prove White’s conjecture for high degrees with respect to the rank. This extends our result (Lasoń and Michałek in Adv Math 259:1–12, 2014) confirming White’s conjecture ‘up to saturation’. Furthermore, we study degrees of Gröbner bases and Betti tables of the toric ideals of matroids of a fixed rank.