Skip to Main content Skip to Navigation
Conference papers

Toric Ideals of Flow Polytopes

Abstract : We show that toric ideals of flow polytopes are generated in degree $3$. This was conjectured by Diaconis and Eriksson for the special case of the Birkhoff polytope. Our proof uses a hyperplane subdivision method developed by Haase and Paffenholz. It is known that reduced revlex Gröbner bases of the toric ideal of the Birkhoff polytope $B_n$ have at most degree $n$. We show that this bound is sharp for some revlex term orders. For $(m \times n)$-transportation polytopes, a similar result holds: they have Gröbner bases of at most degree $\lfloor mn/2 \rfloor$. We construct a family of examples, where this bound is sharp.
Complete list of metadata

Cited literature [11 references]  Display  Hide  Download

https://hal.inria.fr/hal-01186265
Contributor : Coordination Episciences Iam <>
Submitted on : Monday, August 24, 2015 - 3:46:08 PM
Last modification on : Monday, December 28, 2020 - 10:22:04 AM
Long-term archiving on: : Wednesday, November 25, 2015 - 5:11:37 PM

File

dmAN0166.pdf
Publisher files allowed on an open archive

Identifiers

  • HAL Id : hal-01186265, version 1

Collections

Citation

Matthias Lenz. Toric Ideals of Flow Polytopes. 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010), 2010, San Francisco, United States. pp.889-896. ⟨hal-01186265⟩

Share

Metrics

Record views

58

Files downloads

609