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Let $V$ be a vertex operator algebra, $k$ a positive integer and $\sigma$ apermutation automorphism of the vertex operator algebra $V^{\otimes k}$. Inthis paper, we determine the fusion product of any $V^{\otimes k}$-module withany $\sigma$-twisted $V^{\otimes k}$-module.

Fusion products of twisted modules in permutation orbifolds