Powers of componentwise linear ideals
Juergen Herzog, Takayuki Hibi, Hidefumi Ohsugi
TL;DR
This paper establishes criteria for graded ideals to ensure all their powers are componentwise linear, with applications to vertex cover ideals of specific graphs, advancing understanding of ideal properties in algebraic combinatorics.
Contribution
It provides new criteria for componentwise linearity of all powers of graded ideals, including applications to graph-related ideals.
Findings
Criteria for ideals to have all powers componentwise linear
Application to vertex cover ideals of certain graphs
Enhanced understanding of ideal properties in combinatorial algebra
Abstract
We give criteria for graded ideals to have the property that all their powers are componentwise linear. Typical examples to which our criteria can be applied include the vertex cover ideals of certain finite graphs.
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