“School of Mathematics”
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Paper IPM / M / 13374  


Abstract:  
Let \mathbbK be a field, and let R=\mathbbK[x_{1},...,x_{n}] be the
polynomial ring over \mathbbK in n indeterminates x_{1},…,x_{n}.
Let G be a graph with vertexset {x_{1},...,x_{n}}, and let J be the
cover ideal of G in R. For a given positive integer k, we denote the
kth symbolic power and the kth bracket power of J by J^{(k)} and
J^{[k]}, respectively. In this paper, we give necessary and sufficient
conditions for R/J^{k}, R/J^{(k)}, and R/J^{[k]} to be CohenMacaulay.
We also study the limit behavior of the depths of these rings.
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