Search results for " monomial ideals"

showing 4 items of 4 documents

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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Tower sets and other configurations with the Cohen-Macaulay property

2014

Abstract Some well-known arithmetically Cohen–Macaulay configurations of linear varieties in P r as k-configurations, partial intersections and star configurations are generalized by introducing tower schemes. Tower schemes are reduced schemes that are a finite union of linear varieties whose support set is a suitable finite subset of Z + c called tower set. We prove that the tower schemes are arithmetically Cohen–Macaulay and we compute their Hilbert function in terms of their support. Afterwards, since even in codimension 2 not every arithmetically Cohen–Macaulay squarefree monomial ideal is the ideal of a tower scheme, we slightly extend this notion by defining generalized tower schemes …

MonomialTower setBetti sequence; Cohen-Macaulay; Tower setCommutative Algebra (math.AC)Combinatoricssymbols.namesake13H10 14N20 13D40FOS: MathematicsMathematicsmonomial idealsHilbert series and Hilbert polynomialAlgebra and Number TheoryIdeal (set theory)Mathematics::Commutative AlgebraCohen–Macaulay propertyMonomial idealCodimensionBetti sequenceMathematics - Commutative AlgebraTower (mathematics)Arithmetically Cohen-MacaulayCohen-MacaulayPrimary decompositionSettore MAT/02 - AlgebraScheme (mathematics)Hilbert functionsymbolsSettore MAT/03 - GeometriaCohen–Macaulay property monomial ideals Hilbert function.
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ALGEBRE SIMMETRICHE DI ALCUNE CLASSI DI IDEALI MONOMIALI

The purpose of this thesis is the study of the symmetric algebra 〖Sym〗_S (L) of an interesting class of monomial ideals: the ideals L ⊂S=K[x1,...,xn,y1,...,ym] of mixed products in two sets of variables. Recently, this class is been used in order to test some algebraic conjecture, including the conjecture of Eisenbud -Goto, on the symmetric algebra 〖Sym〗_S (L) .Since such conjecture involves fundamental invariants of Sym (L), such as the Krull dimension, the multiplicity and regularity of Castelnuovo-Mumford, it was necessary to calculate these invariants or their bounds. This problem is difficult, but if L is generated by a s-sequence, you can arrive at a concrete result. In the work Mixed…

Settore MAT/02 - Algebragraded algebras symmetric algebras monomial ideals algebraic invariants
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