Depths of Powers of the Edge Ideal of a Tree

2009/08/04 by Morey, Susan · 3 citations
#05C65 #13A17 #13F55 #90C27 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.0908.0553

Abstract

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.

Cited by

• Depth of powers of integrally closed edge ideals of edge-weighted paths
• Depth and regularity of powers of edge ideals of edge-weighted trees
• Depth of the 3-path Ideal of Square of a Path

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