Toric ideals of series and parallel connections of matroids

摘要

In 1980, White conjectured that the toric ideal associated to a matroid is generated by binomials corresponding to a symmetric exchange. In this paper, we prove that classes of matroids for which the toric ideal is generated by quadrics and that has quadratic Grobner bases, are closed under series and parallel extensions, series and parallel connections, and 2-sums.