Search results for "combinatoric"

showing 10 items of 1776 documents

Some properties of [tr(Q2p)]12p with application to linear minimax estimation

1990

Abstract A nondifferentiable minimization problem is considered which occurs in linear minimax estimation. This problem is solved by replacing the nondifferentiable maximal eigenvalue of a real nonnegative definite matrix Q with [tr( Q 2 p )] 1/2 p . It is shown that any descent algorithm with inexact step-length rule can be used to obtain linear minimax estimators for the parameter vector of a parameter-restricted linear model.

Discrete mathematicsNumerical AnalysisAlgebra and Number TheoryMinimization problemLinear modelMathematics::Optimization and ControlMinimaxMinimax approximation algorithmMatrix (mathematics)Discrete Mathematics and CombinatoricsGeometry and TopologyMinimax estimatorDescent algorithmEigenvalues and eigenvectorsMathematicsLinear Algebra and its Applications
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The structure of the state representation of shift invariant controllable and observable group codes

2000

AbstractIn this paper an investigation on the structure of the canonical trellis section of shift invariant, l-controllable and m-observable group codes is carried out. Necessary and sufficient conditions for a set of group homomorphisms in order that they represent the trellis section of this class of codes are established.

Discrete mathematicsNumerical AnalysisAlgebra and Number TheoryObservableCanonical representationsBehavioral analysisGroup codeGroup codesDiscrete Mathematics and CombinatoricsHomomorphismCanonical formGeometry and TopologyInvariant (mathematics)Behavioral approachState representationComputer Science::Information TheoryMathematics
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The Rotation χ-Lattice of Ternary Trees

2001

This paper generalizes to k-ary trees the well-known rotation transformation on binary trees. For brevity, only the ternary case is developped. The rotation on ternary trees is characterized using some codings of trees. Although the corresponding poset is not a lattice, we show that it is a χ-lattice in the sense of Leutola–Nieminen. Efficient algorithms are exhibited to compute meets and joins choosen in a particular way.

Discrete mathematicsNumerical AnalysisBinary treeTernary treeWeight-balanced treeComputer Science ApplicationsTheoretical Computer ScienceCombinatoricsComputational MathematicsComputational Theory and MathematicsTernary search treeTernary operationTamari latticePartially ordered setRotation (mathematics)SoftwareMathematicsComputing
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On the Bishop–Phelps–Bollobás theorem for multilinear mappings

2017

Abstract We study the Bishop–Phelps–Bollobas property and the Bishop–Phelps–Bollobas property for numerical radius. Our main aim is to extend some known results about norm or numerical radius attaining operators to multilinear and polynomial cases. We characterize the pair ( l 1 ( X ) , Y ) to have the BPBp for bilinear forms and prove that on L 1 ( μ ) the numerical radius and the norm of a multilinear mapping are the same. We also show that L 1 ( μ ) fails the BPBp-nu for multilinear mappings although L 1 ( μ ) satisfies it in the operator case for every measure μ.

Discrete mathematicsNumerical AnalysisMultilinear mapAlgebra and Number Theory010102 general mathematicsBilinear form01 natural sciences010101 applied mathematicsOperator (computer programming)Discrete Mathematics and CombinatoricsGeometry and Topology0101 mathematicsBishop–Phelps theoremMathematicsLinear Algebra and its Applications
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On the ∗-cocharacter sequence of 3×3 matrices

2000

Abstract Let M 3 (F) be the algebra of 3×3 matrices with involution * over a field F of characteristic zero. We study the ∗ -polynomial identities of M 3 (F) , where ∗=t is the transpose involution, through the representation theory of the hyperoctahedral group B n . After decomposing the space of multilinear ∗ -polynomial identities of degree n under the B n -action, we determine which irreducible B n -modules appear with non-zero multiplicity. In symbols, we write the nth ∗ -cocharacter χ n (M 3 (F),*)=∑ r=0 n ∑ λ⊢r,h(λ)⩽6 μ⊢n−r,h(μ)⩽3 m λ,μ χ λ,μ , where λ and μ are partitions of r and n−r , respectively, χ λ,μ is the irreducible B n -character associated to the pair (λ,μ) and m λ,μ ⩾0 i…

Discrete mathematicsNumerical AnalysisMultilinear mapAlgebra and Number TheoryMultiplicity (mathematics)Hyperoctahedral groupRepresentation theoryPolynomial identitiesCombinatoricsMatrices with involutionCocharacter sequenceDiscrete Mathematics and CombinatoricsGeometry and TopologyMathematicsLinear Algebra and its Applications
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Fixed points and completeness on partial metric spaces

2015

Recently, Suzuki [T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc. 136 (2008), 1861-1869] proved a fixed point theorem that is a generalization of the Banach contraction principle and characterizes the metric completeness. Paesano and Vetro [D. Paesano and P. Vetro, Suzuki's type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces, Topology Appl., 159 (2012), 911-920] proved an analogous fixed point result for a selfmapping on a partial metric space that characterizes the partial metric 0-completeness. In this paper we prove a fixed point result for a new class of…

Discrete mathematicsNumerical AnalysisPartial metric 0-completeneControl and OptimizationAlgebra and Number TheoryPartial metric spaceInjective metric spaceOrdered partial metric spaceEquivalence of metricsConvex metric spaceIntrinsic metricMetric spaceSettore MAT/05 - Analisi MatematicaSuzuki fixed point theoremCompleteness (order theory)Metric (mathematics)Discrete Mathematics and CombinatoricsMetric mapFixed and common fixed pointAnalysisMathematicsMiskolc Mathematical Notes
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Ordinary and graded cocharacter of the Jordan algebra of 2x2 upper triangular matrices

2014

Abstract Let F be a field of characteristic zero and U J 2 ( F ) be the Jordan algebra of 2 × 2 upper triangular matrices over F . In this paper we give a complete description of the space of multilinear graded and ordinary identities in the language of Young diagrams through the representation theory of a Young subgroup of S n . For every Z 2 -grading of U J 2 ( F ) we compute the multiplicities in the graded cocharacter sequence and furthermore we compute the ordinary cocharacter.

Discrete mathematicsNumerical AnalysisSequenceMultilinear mapPure mathematicsAlgebra and Number TheoryJordan algebraZero (complex analysis)Triangular matrixField (mathematics)Space (mathematics)Representation theoryJordan algebras Polynomial identities Basis of identities Cocharacter Gradings Graded polynomial identitiesSettore MAT/02 - AlgebraDiscrete Mathematics and CombinatoricsGeometry and TopologyMathematics
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Fine and Wilf's Theorem for Three periods and a Generalization of Sturmian Words

1999

AbstractWe extend the theorem of Fine and Wilf to words having three periods. We then define the set 3-PER of words of maximal length for which such result does not apply. We prove that the set 3-PER and the sequences of complexity 2n + 1, introduced by Arnoux and Rauzy to generalize Sturmian words, have the same set of factors.

Discrete mathematicsPeriodicityEuclid's algorithmCombinatorics on wordsGeneral Computer ScienceGeneralizationSturmian wordSturmian wordsTheoretical Computer ScienceCombinatoricsSet (abstract data type)Combinatorics on wordsWord lengthComputer Science(all)Mathematics
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A note on the packing of two copies of some trees into their third power

2003

Abstract It is proved in [1] that if a tree T of order n is not a star, then there exists an edge-disjoint placement of two copies of this tree into its fourth power. In this paper, we prove the packing of some trees into their third power.

Discrete mathematicsPermutationFourth powerApplied MathematicsA* search algorithmlaw.inventionPackingCombinatoricslawOrder (group theory)Tree (set theory)Power treeEmbeddingPlacementMathematicsApplied Mathematics Letters
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Graphs of stable maps from closed surfaces to the projective plane

2018

Abstract We describe how to attach a weighted graph to each stable map from closed surfaces to projective plane and prove that any weighted graph with non negatively weighted vertices is the graph of some stable map from a closed surface to the projective plane.

Discrete mathematicsPlane curve010102 general mathematicsLine at infinity01 natural sciencesPlanar graph010101 applied mathematicsCombinatoricssymbols.namesakeBlocking setReal projective planesymbolsProjective spaceGeometry and TopologyProjective plane0101 mathematicsPencil (mathematics)MathematicsTopology and its Applications
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