40 research outputs found
The toric ideal of a graphic matroid is generated by quadrics
Describing minimal generating sets of toric ideals is a well-studied and
difficult problem. Neil White conjectured in 1980 that the toric ideal
associated to a matroid is generated by quadrics corresponding to single
element symmetric exchanges. We give a combinatorial proof of White's
conjecture for graphic matroids.Comment: 19 pages, 4 figure
Toric Ideals of Lattice Path Matroids and Polymatroids
We show that the toric ideal of a lattice path polymatroid is generated by
quadrics corresponding to symmetric exchanges, and give a monomial order under
which these quadrics form a Gr\"obner basis. We then obtain an analogous result
for lattice path matroids.Comment: 9 pages, 4 figure