Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Minimal systems of binomial generators and the indispensable complex of
  a toric ideal   Let $A=\{{\bf a}_1,...,{\bf a}_m\} \subset \mathbb{Z}^n$ be a vector
configuration and $I_A \subset K[x_1,...,x_m]$ its corresponding toric ideal.
The paper consists of two parts. In the first part we completely determine the
number of different minimal systems of binomial generators of $I_A$. We also
prove that generic toric ideals are generated by indispensable binomials. In
the second part we associate to $A$ a simplicial complex $\Delta _{\ind(A)}$.
We show that the vertices of $\Delta_{\ind(A)}$ correspond to the indispensable
monomials of the toric ideal $I_A$, while one dimensional facets of
$\Delta_{\ind(A)}$ with minimal binomial $A$-degree correspond to the
indispensable binomials of $I_{A}$.

27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an