Monomial Ideals, Computations and Applications

Let G be a graph with n vertices and S = K[x 1 , . . . , x n ] be the polynomial ring in n variables over a field K. Assume that J(G) is the cover ideal of G and J(G) (k) is its k-th symbolic power. We prove that if G is a very well-covered graph such that J(G) has linear resolution, then J(G) (k) has linear resolution, for every integer k ≥ 1. We also prove that for a every very well-covered graph G, the depth of symbolic powers of J(G) forms a non-increasing sequence. Finally, we determine a linear upper bound for the regularity of powers of cover ideal of bipartite graph.

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Monomial Ideals, Computations and Applications

Cited by 5 publications

References 107 publications

On Invariants of Modules over the Ring of Differential Operators

On Invariants of Modules over the Ring of Differential Operators

On the Stanley Depth and Size of Monomial Ideals

Symbolic powers of cover ideal of very well-covered and bipartite graphs

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