Componentwise linear ideals and exchange properties
Ayesha Asloob Qureshi, Somayeh Bandari
TL;DR
This paper investigates the conditions under which certain ideals, related to hypergraphs and polymatroidal structures, are componentwise linear, providing new insights into their algebraic and combinatorial properties.
Contribution
It introduces a new exchange property that ensures componentwise linearity of ideals, extending known results to hypergraph cover ideals.
Findings
Proves componentwise linearity for ideals satisfying the exchange property.
Analyzes componentwise linearity of ideals of k-covers of hypergraphs.
Establishes connections between exchange properties and algebraic structure.
Abstract
We prove the componentwise linearity of ideals that satisfy a certain exchange property similar to polymatroidal ideals. We also discuss the componentwise linearity and exchange properties of ideals of -covers of totally balanced weighted hypergraphs.
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Taxonomy
TopicsRings, Modules, and Algebras · Commutative Algebra and Its Applications · Advanced Algebra and Logic