Search results for "13F55"

showing 3 items of 3 documents

In the Shadows of a hypergraph: looking for associated primes of powers of squarefree monomial ideals

2018

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 contai…

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 13C99
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Steiner configurations ideals: Containment and colouring

2021

Given a homogeneous ideal I&sube

HypergraphSteiner systemsCurrent (mathematics)General MathematicsIdeals of points Monomial ideals Steiner systems Symbolic powers of ideals Waldschmidt constantideals of points0102 computer and information sciencesCommutative Algebra (math.AC)01 natural sciencesCombinatoricsMathematics - Algebraic GeometryMonomial idealsFOS: MathematicsComputer Science (miscellaneous)Mathematics - Combinatorics13F55 13F20 14G50 51E10 94B270101 mathematicsAlgebraic Geometry (math.AG)Engineering (miscellaneous)MathematicsSymbolic powers of idealsmonomial idealsContainment (computer programming)ConjectureIdeal (set theory)Mathematics::Commutative Algebralcsh:Mathematics010102 general mathematicslcsh:QA1-939Mathematics - Commutative AlgebraIdeals of pointsWaldschmidt constantComplement (complexity)Settore MAT/02 - AlgebraSteiner systemCover (topology)010201 computation theory & mathematicssymbolic powers of idealsIdeals of points; Monomial ideals; Steiner systems; Symbolic powers of ideals; Waldschmidt constantCombinatorics (math.CO)Settore MAT/03 - Geometriamonomial ideals ideals of points symbolic powers of ideals Waldschmidt constant Steiner systems
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Steiner systems and configurations of points

2020

AbstractThe aim of this paper is to make a connection between design theory and algebraic geometry/commutative algebra. In particular, given any Steiner SystemS(t, n, v) we associate two ideals, in a suitable polynomial ring, defining a Steiner configuration of points and its Complement. We focus on the latter, studying its homological invariants, such as Hilbert Function and Betti numbers. We also study symbolic and regular powers associated to the ideal defining a Complement of a Steiner configuration of points, finding its Waldschmidt constant, regularity, bounds on its resurgence and asymptotic resurgence. We also compute the parameters of linear codes associated to any Steiner configur…

Linear codes; Monomial ideals; Stanley Reisner rings; Steiner systems; Symbolic powersSteiner systemsBetti numberPolynomial ring0102 computer and information sciencesAlgebraic geometrySymbolic powers01 natural sciencessymbols.namesakeMathematics - Algebraic GeometryLinear codesTheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITYMonomial idealsComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONFOS: MathematicsMathematics - CombinatoricsIdeal (ring theory)0101 mathematicsCommutative algebraAlgebraic Geometry (math.AG)Complement (set theory)MathematicsDiscrete mathematicsHilbert series and Hilbert polynomialApplied Mathematics010102 general mathematicsStanley Reisner ringsLinear codes Monomial ideals Stanley Reisner rings Steiner systems Symbolic powersComputer Science Applications51E10 13F55 13F20 14G50 94B27Settore MAT/02 - AlgebraSteiner systemSteiner systems Monomial ideals Symbolic powers Stanley Reisner rings Linear codes010201 computation theory & mathematicssymbolsCombinatorics (math.CO)Settore MAT/03 - GeometriaMathematicsofComputing_DISCRETEMATHEMATICS
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