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Toric Ideals Generated by Circuits

    https://doi.org/10.1142/S1005386712000533Cited by:7 (Source: Crossref)

    Let be the toric ideal of a homogeneous normal configuration . We prove that is generated by circuits if and only if each unbalanced circuit of has a connector which is a linear combination of circuits with a square-free term. In particular, if each circuit of with non-square-free terms is balanced, then is generated by circuits. As a consequence, we prove that the toric ideal of a normal edge subring of a multigraph is generated by circuits with a square-free term.

    AMSC: 13H10, 13B22, 13F20, 05B35