Matching powers of monomial ideals and edge ideals of weighted oriented graphs

We introduce the concept of matching powers of monomial ideals. Let [Formula: see text] be a monomial ideal of [Formula: see text], where [Formula: see text] is a field. The [Formula: see text]th matching power of [Formula: see text] is the monomial ideal [Formula: see text] generated by the products [Formula: see text] where [Formula: see text] is a sequence of support-disjoint monomials contained in [Formula: see text]. This concept naturally generalizes the notion of squarefree powers of squarefree monomial ideals. We study the normalized depth function of matching powers of monomial ideals and provide bounds for the regularity and projective dimension of edge ideals of weighted oriented graphs. When [Formula: see text] is a non-quadratic edge ideal of a weighted oriented graph that contains no even cycles, we characterize when [Formula: see text] has a linear resolution.