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This article explores a novel operation of a monomial ideal, termed duplication, which produces a monomial ideal I^ I ⋄ from another I . This operation is inspired by and generalizes how vertex duplication affects the edge ideal of a graph. The main result describes a multigraded minimal free resolution of I^ I ⋄ as long as we know a resolution for I . Consequently, we obtain formulas for the projective dimension and depth of I^ I ⋄ in terms of the corresponding invariants of I .
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Valencia et al. (2024) studied this question.
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