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Pf is generated by a finite set of circuits

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Reference no: EM131587381

Question: In the proof of Theorem (from (c) to (a)), show that the subcases (A3), (B1), and (B3) cannot occur.

Theorem: If K[F] is homogeneous and normal and PF is its toric ideal, then the following are equivalent:

(a) PF is generated by a finite set of circuits.

(b) PF is generated by a finite set of circuits with a square-free term.

(c) Every unbalanced circuit of PF has a connector which is a linear combination (with coefficients in K[t]) of circuits of PF with a square-free term.

Reference no: EM131587381

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