Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Toric Ideals of Flow Polytopes   A referee found an error in the proof of the Main Theorem ("toric ideals of
flow polytopes are generated in degree 3") that we could not fix. More
precisely, the proof of Lemma 4.2.(ii) is incorrect.
  The results on Gr\"obner bases are untouched by this.
  -----
  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 Gr\"obner 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 Gr\"obner bases of at most degree $\lfloor
mn/2\rfloor$. We construct a family of examples, where this bound is sharp.

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The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
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The categories of this paper are: econ