On the toric ideal of a matroid
By Michal Laso'n, M. Michałek. 2013
49 citations recorded by the source corpus.
Abstract 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.
Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/7b4fa54d0cef92b1e51634fbe24e4e256b396d59
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In Algebra and Number Theory
In Computational Theory and Mathematics
- Lindsay C. Piechnik
- Francisco Santos
- Christian Haase
- Andreas Paffenholz
- Alexander Postnikov
- M. Develin
- Federico Ardila
- Bernd Sturmfels
In Geometry and Topology
Citations in the corpus
- Existence of unimodular triangulations — positive results (2014, background): “ass of matroid polytopes and thus could shed some light on an old conjecture of Neil White [138] that the toric ideal of a matroid polytope is generated in degree two. A partial positive answer is in [79], but a quadratic triangulation of the matroid polytope would even yield a quadratic Gro¨bner ba”