5 research outputs found
Minimal systems of binomial generators and the indispensable complex of a toric ideal
Let be a vector
configuration and 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 . We also
prove that generic toric ideals are generated by indispensable binomials. In
the second part we associate to a simplicial complex \Delta _{\ind(A)}.
We show that the vertices of \Delta_{\ind(A)} correspond to the indispensable
monomials of the toric ideal , while one dimensional facets of
\Delta_{\ind(A)} with minimal binomial -degree correspond to the
indispensable binomials of