Depths of Powers of the Edge Ideal of a Tree |
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| Authors: | Susan Morey |
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| Institution: | 1. Department of Mathematics , Texas State University , San Marcos, Texas, USA morey@txstate.edu |
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| Abstract: | Lower bounds are given for the depths of R/I t for t ≥ 1 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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| Keywords: | Depth Edge ideal Monomial ideal Powers of ideals Tree |
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