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Quadratic Gröbner bases for cut ideals of cycles and ring graphs
Let $C_n$ be the cycle of length $n\ge3$ and let $I_{C_n}$ be its cut ideal. We show that $I_{C_n}$ has a quadratic Gröbner basis with respect to an explicit weight order. Since the defining configuration consists of $(0,1)$-vectors, the initial monomials of such a basis are automatically squarefree
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