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For a monomial ideal $I$, let $G(I)$ be its minimal set of monomialgenerators. If there is a total order on $G(I)$ such that the correspondingLyubeznik resolution of $I$ is a minimal free resolution of $I$, then $I$ iscalled a Lyubeznik ideal. In this paper, we characterize the Lyubeznik ideals,and we discover some classes of Lyubeznik ideals.

On monomial ideals whose Lyubeznik resolution is minimal