The edge ideals of $\mathbf{t}$-spread $d$-partite hypergraphs

Abstract

Inspired by the definition of $\mathbf{t}$-spread monomial ideals, in this paper, we introduce $\mathbf{t}$-spread $d$-partite hypergraph $K_V^{\mathbf{t}}$ and study its edge ideal $I(K_V^{\mathbf{t}})$. We prove that $I(K_V^{\mathbf{t}})$ has linear quotients, all powers of $I(K_V^{\mathbf{t}})$ have linear resolution and the Rees algebra of $I(K_V^{\mathbf{t}})$ is a normal Cohen-Macaulay domain. It is also shown that $I(K_V^{\mathbf{t}})$ is normally torsion-free and a complete characterization of Cohen-Macaulay $S/I(K_V^{\mathbf{t}})$ is given.

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