Asymptotic depth of invariant chains of edge ideals
Commutative Algebra
2024-09-11 v1 Combinatorics
Abstract
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.
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Cite
@article{arxiv.2409.06252,
title = {Asymptotic depth of invariant chains of edge ideals},
author = {Tran Quang Hoa and Do Trong Hoang and Dinh Van Le and Hop D. Nguyen and Thai Thanh Nguyen},
journal= {arXiv preprint arXiv:2409.06252},
year = {2024}
}
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33 pages