Search results for "Steiner system"

showing 4 items of 4 documents

On n–Fold Blocking Sets

1986

An n-fold blocking set is a set of n-disjoint blocking sets. We shall prove upper and lower bounds for the number of components in an n-fold blocking set in projective and affine spaces.

Discrete mathematicsSet (abstract data type)CombinatoricsQuantitative Biology::BiomoleculesSteiner systemBlocking setFold (higher-order function)Blocking (radio)Projective planeAffine transformationUpper and lower boundsMathematics
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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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An algebraic representation of Steiner triple systems of order 13

2021

Abstract In this paper we construct an incidence structure isomorphic to a Steiner triple system of order 13 by defining a set B of twentysix vectors in the 13-dimensional vector space V = GF ( 5 ) 13 , with the property that there exist precisely thirteen 6-subsets of B whose elements sum up to zero in V , which can also be characterized as the intersections of B with thirteen linear hyperplanes of V .

Steiner triple systemZero (complex analysis)Steiner triple system STS Additive block designSTSCombinatoricsSet (abstract data type)Steiner systemIncidence structureHyperplaneSettore MAT/05 - Analisi MatematicaAlgebra representationQA1-939Order (group theory)Settore MAT/03 - GeometriaMathematicsVector spaceMathematicsAdditive block designExamples and Counterexamples
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