Asymptotic depth of invariant chains of edge ideals

We completely determine the asymptotic depth, equivalently, the asymptotic projective dimension of a chain of edge ideals that is invariant under the action of the monoid Inc of increasing functions on the positive integers. Our results and their proofs also reveal surprising combinatorial and topol...

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Bibliographic Details
Published in:arXiv.org 2024-09
Main Authors: Tran, Quang Hoa, Do Trong Hoang, Dinh Van Le, Nguyen, Hop D, Thai Thanh Nguyen
Format: Article
Language:English
Subjects:
Asymptotic properties
Combinatorial analysis
Homology
Invariants
Monoids
Online Access:Get full text
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Summary:We completely determine the asymptotic depth, equivalently, the asymptotic projective dimension of a chain of edge ideals that is invariant under the action of the monoid Inc of increasing functions on the positive integers. Our results and their proofs also reveal surprising combinatorial and topological properties of corresponding graphs and their independence complexes. In particular, we are able to determine the asymptotic behavior of all reduced homology groups of these independence complexes.
ISSN:2331-8422