Depths of Powers of the Edge Ideal of a Tree

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...

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Bibliographic Details
Published inCommunications in algebra Vol. 38; no. 11; pp. 4042 - 4055
Main Author Morey, Susan
Format Journal Article
LanguageEnglish
Published Taylor & Francis Group 15.11.2010
Subjects
Algebra
Depth
Edge ideal
Forests
Lower bounds
Monomial ideal
Powers of ideals
Tree
Trees
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Summary: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.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0092-7872
1532-4125
DOI:10.1080/00927870903286900