Search results for "combinatoric"

showing 10 items of 1776 documents

Three-page encoding and complexity theory for spatial graphs

2004

We construct a series of finitely presented semigroups. The centers of these semigroups encode uniquely up to rigid ambient isotopy in 3-space all non-oriented spatial graphs. This encoding is obtained by using three-page embeddings of graphs into the product of the line with the cone on three points. By exploiting three-page embeddings we introduce the notion of the three-page complexity for spatial graphs. This complexity satisfies the properties of finiteness and additivity under natural operations.

Discrete mathematics[ MATH.MATH-GT ] Mathematics [math]/Geometric Topology [math.GT]Algebra and Number TheoryDegree (graph theory)Semigroup010102 general mathematicsGeometric topologyGeometric Topology (math.GT)01 natural sciences57M25 57M15 57M05Combinatorics010104 statistics & probabilityMathematics - Geometric TopologyCone (topology)Additive functionEncoding (memory)[MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT]FOS: Mathematics0101 mathematicsUnit (ring theory)Ambient isotopyMathematics[MATH.MATH-GT] Mathematics [math]/Geometric Topology [math.GT]MathematicsofComputing_DISCRETEMATHEMATICS
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Three cyclic branched covers suffice to determine hyperbolic knots.

2005

Let n > m > 2 be two fixed coprime integers. We prove that two Conway reducible, hyperbolic knots sharing the 2-fold, m-fold and n-fold cyclic branched covers are equivalent. Using previous results by Zimmermann we prove that this implies that a hyperbolic knot is determined by any three of its cyclic branched covers.

Discrete mathematics[ MATH.MATH-GT ] Mathematics [math]/Geometric Topology [math.GT]Quantitative Biology::BiomoleculesAlgebra and Number TheoryCoprime integers010102 general mathematics01 natural sciencesMathematics::Geometric TopologyCombinatoricsKnot (unit)[MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT]0103 physical sciences010307 mathematical physics0101 mathematics[MATH.MATH-GT] Mathematics [math]/Geometric Topology [math.GT]Mathematics
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New Encodings of Pseudo-Boolean Constraints into CNF

2009

International audience; This paper answers affirmatively the open question of the existence of a polynomial size CNF encoding of pseudo-Boolean (PB) constraints such that generalized arc consistency (GAC) is maintained through unit propagation (UP). All previous encodings of PB constraints either did not allow UP to maintain GAC, or were of exponential size in the worst case. This paper presents an encoding that realizes both of the desired properties. From a theoretical point of view, this narrows the gap between the expressive power of clauses and the one of pseudo-Boolean constraints.

Discrete mathematics[INFO.INFO-CC]Computer Science [cs]/Computational Complexity [cs.CC]Polynomial021103 operations researchUnit propagation[INFO.INFO-DS]Computer Science [cs]/Data Structures and Algorithms [cs.DS]0211 other engineering and technologies[INFO.INFO-DS] Computer Science [cs]/Data Structures and Algorithms [cs.DS]02 engineering and technologyComputer Science::Computational ComplexityExpressive powerExponential functionCombinatorics[ INFO.INFO-CC ] Computer Science [cs]/Computational Complexity [cs.CC]Encoding (memory)0202 electrical engineering electronic engineering information engineeringLocal consistency020201 artificial intelligence & image processingPoint (geometry)[INFO.INFO-CC] Computer Science [cs]/Computational Complexity [cs.CC][ INFO.INFO-DS ] Computer Science [cs]/Data Structures and Algorithms [cs.DS]Mathematics
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Elements with square roots in compact groups

2010

The probability that a randomly chosen element has a square root is studied in [1, 2, 8] in the finite case. Here we deal with the infinite case.

Discrete mathematicselements with square rootFunctional square rootGeneral MathematicsprobabilityFinite casecompact groupsUnit squareCombinatoricsSettore MAT/02 - AlgebraSquare rootSettore MAT/05 - Analisi MatematicaSettore MAT/03 - GeometriaElement (category theory)Square numberMathematics
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Finitary Representations and Images of Transitive Finitary Permutation Groups

1999

Abstract We characterize the point stabilizers and kernels of finitary permutation representations of infinite transitive groups of finitary permutations. Moreover, the number of such representations is determined.

Discrete mathematicshomomorphic imagesMathematics::CombinatoricsAlgebra and Number Theorypermutation groupsfinitary groupsBit-reversal permutationGeneralized permutation matrixPermutation groupCyclic permutationCombinatoricsMathematics::LogicPermutationwreath productsWreath productMathematics::Category TheoryComputer Science::Logic in Computer ScienceFinitaryPermutation graphMathematicsJournal of Algebra
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Set-valued mappings in partially ordered fuzzy metric spaces

2014

Abstract In this paper, we provide coincidence point and fixed point theorems satisfying an implicit relation, which extends and generalizes the result of Gregori and Sapena, for set-valued mappings in complete partially ordered fuzzy metric spaces. Also we prove a fixed point theorem for set-valued mappings on complete partially ordered fuzzy metric spaces which generalizes results of Mihet and Tirado. MSC:54E40, 54E35, 54H25.

Discrete mathematicspartially ordered setApplied MathematicsInjective metric spaceset-valued mappingT-normFixed-point propertyConvex metric spaceLeast fixed pointcoincidence pointfixed pointSettore MAT/05 - Analisi MatematicaDiscrete Mathematics and CombinatoricsDomain theoryfuzzy metric spaceFilter (mathematics)Coincidence pointAnalysisMathematics
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The Hamilton–Jacobi Equation

2001

We already know that canonical transformations are useful for solving mechanical problems. We now want to look for a canonical transformation that transforms the 2N coordinates (q i , p i ) to 2N constant values (Q i , P i ), e.g., to the 2N initial values \((q_{i}^{0},p_{i}^{0})\) at time t = 0. Then the problem would be solved, q = q(q0, p0, t), p = p(q0, p0, t).

Dispersionless equationCombinatoricsPhysicsOmega equationCharacteristic equationCanonical transformationSummation equationCahn–Hilliard equationKadomtsev–Petviashvili equationHamilton–Jacobi equation
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Periodic and quasi-periodic orbits of the dissipative standard map

2011

We present analytical and numerical investigations of the dynamics of the dissipative standard map. We first study the existence of periodic orbits by using a constructive version of the implicit function theorem; then, we introduce a parametric representation, which provides the interval of the drift parameter ensuring the existence of a periodic orbit with a given period. The determination of quasi--periodic attractors is efficiently obtained using the parametric representation combined with a Newton's procedure, aimed to reduce the error of the approximate solution provided by the parametric representation. These methods allow us to relate the drift parameter of the periodic orbits to th…

Dissipative standard mapApplied MathematicsMathematical analysisArnold's tonguesPeriodic sequenceStandard mapParameter spaceImplicit function theoremAttractorDissipative systemDiscrete Mathematics and CombinatoricsPeriodic orbitsArnold's tongues; Dissipative standard map; Periodic orbits; Discrete Mathematics and Combinatorics; Applied MathematicsInvariant (mathematics)Dissipative standard map; Periodic orbits; Arnold's tonguesSettore MAT/07 - Fisica MatematicaParametric statisticsMathematics
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On multiples of divisors associated to Veronese embeddings with defective secant variety

2009

In this note we consider multiples aD, where D is a divisor of the blow-up of P^n along points in general position which appears in the Alexander and Hirschowitz list of Veronese embeddings having defective secant varieties. In particular we show that there is such a D with h^1(X,D) > 0 and h^1(X,2D) = 0.

DivisorGeneral MathematicsLinear systemLinear systems14C20CombinatoricsMathematics - Algebraic GeometrySecant varietyLinear systems fat pointsFOS: MathematicsSettore MAT/03 - Geometriafat pointsAlgebraic Geometry (math.AG)General positionMultipleMathematics
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Longest Common Subsequence from Fragments via Sparse Dynamic Programming

1998

Sparse Dynamic Programming has emerged as an essential tool for the design of efficient algorithms for optimization problems coming from such diverse areas as Computer Science, Computational Biology and Speech Recognition [7,11,15]. We provide a new Sparse Dynamic Programming technique that extends the Hunt-Szymanski [2,9,8] paradigm for the computation of the Longest Common Subsequence (LCS) and apply it to solve the LCS from Fragments problem: given a pair of strings X and Y (of length n and m, resp.) and a set M of matching substrings of X and Y, find the longest common subsequence based only on the symbol correspondences induced by the substrings. This problem arises in an application t…

Dynamic programmingCombinatoricsSet (abstract data type)Longest common subsequence problemOptimization problemMatching (graph theory)Combinatorial optimizationData structureSubstringMathematics
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