6533b85efe1ef96bd12bf3a2
RESEARCH PRODUCT
In the Shadows of a hypergraph: looking for associated primes of powers of squarefree monomial ideals
Erin BelaGiuseppe FavacchioNghia T.h. Transubject
HypergraphMonomialProperty (philosophy)Associated primes Cover ideals Hypergraphs Powers of idealsMathematics::Number Theory0102 computer and information sciencesHypergraphsCommutative Algebra (math.AC)01 natural sciencesCover idealsCombinatoricsSimple (abstract algebra)FOS: MathematicsMathematics - CombinatoricsDiscrete Mathematics and CombinatoricsPowers of ideals0101 mathematicsMathematicsAlgebra and Number TheoryIdeal (set theory)Mathematics::Commutative Algebra010102 general mathematicsAssociated primes; Cover ideals; Hypergraphs; Powers of idealsMonomial idealSquare-free integerMathematics - Commutative AlgebraSettore MAT/02 - AlgebraCover (topology)010201 computation theory & mathematicsAssociated primesSettore MAT/03 - GeometriaCombinatorics (math.CO)05C65 13F55 05E99 13C99description
The aim of this paper is to study the associated primes of powers of square-free monomial ideals. Each square-free monomial ideal corresponds uniquely to a finite simple hypergraph via the cover ideal construction, and vice versa. Let H be a finite simple hypergraph and J(H) the cover ideal of H. We define the shadows of hypergraph, H, described as a collection of smaller hypergraphs related to H under some conditions. We then investigate how the shadows of H preserve information about the associated primes of the powers of J(H). Finally, we apply our findings on shadows to study the persistence property of square-free monomial ideals and construct some examples exhibiting failure of containment.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2018-09-24 |