Depth stability of cover ideals

Let R = K[x1,...,xr] be a polynomial ring over a field K. Let G be a graph with vertex set {1,...,r} and let J be the cover ideal of G. We give a sharp bound for the stability index of symbolic depth function sdstab(J). In the case G is bipartite, it yields a sharp bound for the stability index of d...

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Bibliographic Details
Published in:arXiv.org 2022-10
Main Authors: Mai, Phuoc Binh, Nguyen, Thu Hang, Truong Thi Hien, Tran, Nam Trung
Format: Article
Language:English
Subjects:
Polynomials
Rings (mathematics)
Stability
Vertex sets
Online Access:Get full text
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Summary:Let R = K[x1,...,xr] be a polynomial ring over a field K. Let G be a graph with vertex set {1,...,r} and let J be the cover ideal of G. We give a sharp bound for the stability index of symbolic depth function sdstab(J). In the case G is bipartite, it yields a sharp bound for the stability index of depth function dstab(J) and this bound is exact if G is a forest.
ISSN:2331-8422