Depths of Powers of the Edge Ideal of a Tree
classification
🧮 math.AC
keywords
boundsdepthslowertreeconnecteddiameteredgeforest
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Lower bounds are given for the depths of R/I^t for t at least one when I is the edge ideal of a tree or forest. The bounds are given in terms of the diameter of the tree, or in case of a forest, the largest diameter of a connected component and the number of connected components. These lower bounds provide a lower bound on the power for which the depths stabilize.
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