Search results for "abstract"

showing 10 items of 1959 documents

When can an equational simple graph be generated by hyperedge replacement?

1998

Infinite hypergraphs with sources arise as the canonical solutions of certain systems of recursive equations written with operations on hypergraphs. There are basically two different sets of such operations known from the literature, HR and VR. VR is strictly more powerful than HR on simple hypergraphs. Necessary conditions are known ensuring that a VR-equational simple hypergraph is also HR-equational. We prove that two of them, namely having finite tree-width or not containing the infinite bipartite graph, are also sufficient. This shows that equational hypergraphs behave like context-free sets of finite hypergraphs.

CombinatoricsDiscrete mathematicsHypergraphGraph rewritingMathematics::CombinatoricsSimple graphBinary treeComputer Science::Discrete MathematicsSimple (abstract algebra)Bipartite graphKleene's recursion theoremHomomorphismMathematics
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A Loopless Generation of Bitstrings without p Consecutive Ones

2001

Let F n (p) be the set of all n-length bitstrings such that there are no p consecutive ls. F n (p) is counted with the pth order Fibonacci numbers and it may be regarded as the subsets of {1, 2,…, n} without p consecutive elements and bitstrings in F n (p) code a particular class of trees or compositions of an integer. In this paper we give a Gray code for F n (p) which can be implemented in a recursive generating algorithm, and finally in a loopless generating algorithm.

CombinatoricsGray codeSet (abstract data type)Discrete mathematicssymbols.namesakeCode (set theory)Fibonacci numberBinary treeIntegersymbolsOrder (group theory)Hamiltonian pathMathematics
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Orientation matters

2008

The optimal communication spanning tree (OCST) problem is a well known $\mathcal{NP}$-hard combinatorial optimization problem which seeks a spanning tree that satisfies all given communication requirements for minimal total costs. It has been shown that optimal solutions of OCST problems are biased towards the much simpler minimum spanning tree (MST) problem. Therefore, problem-specific representations for EAs like heuristic variants of edge-sets that are biased towards MSTs show high performance.In this paper, additional properties of optimal solutions for Euclidean variants of OCST problems are studied. Experimental results show that not only edges in optimal trees are biased towards low-…

CombinatoricsMathematical optimizationSpanning treeHeuristicCrossoverEvolutionary algorithmGraph (abstract data type)Orientation (graph theory)Minimum spanning treeHeuristicsMathematicsofComputing_DISCRETEMATHEMATICSMathematicsProceedings of the 10th annual conference on Genetic and evolutionary computation
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Computing the Kekulé structure count for alternant hydrocarbons

2002

A fast computer algorithm brings computation of the permanents of sparse matrices, specifically, molecular adjacency matrices. Examples and results are presented, along with a discussion of the relationship of the permanent to the Kekule structure count. A simple method is presented for determining the Kekule structure count of alternant hydrocarbons. For these hydrocarbons, the square of the Kekule structure count is equal to the permanent of the adjacency matrix. In addition, for alternant structures the adjacency matrix for N atoms can be written in such a way that only an N/2 × N/2 matrix need be evaluated. The Kekule structure count correlates with topological indices. The inclusion of…

CombinatoricsMatrix (mathematics)Alternant hydrocarbonLogarithmSimple (abstract algebra)Adjacency matrixPhysical and Theoretical ChemistryCondensed Matter PhysicsAtomic and Molecular Physics and OpticsOrder of magnitudeSquare (algebra)MathematicsSparse matrixInternational Journal of Quantum Chemistry
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Quantum Query Complexity for Some Graph Problems

2004

The paper [4] by H. Buhrman and R. de Wolf contains an impressive survey of solved and open problems in quantum query complexity, including many graph problems. We use recent results by A.Ambainis [1] to prove higher lower bounds for some of these problems. Some of our new lower bounds do not close the gap between the best upper and lower bounds. We prove in these cases that it is impossible to provide a better application of Ambainis’ technique for these problems.

CombinatoricsQuantum queryGraph (abstract data type)Computer Science::Computational ComplexityUpper and lower boundsMathematics
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Structured Frequency Algorithms

2015

B.A. Trakhtenbrot proved that in frequency computability (introduced by G. Rose) it is crucially important whether the frequency exceeds \(\frac{1}{2}\). If it does then only recursive sets are frequency-computable. If the frequency does not exceed \(\frac{1}{2}\) then a continuum of sets is frequency-computable. Similar results for finite automata were proved by E.B. Kinber and H. Austinat et al. We generalize the notion of frequency computability demanding a specific structure for the correct answers. We show that if this structure is described in terms of finite projective planes then even a frequency \(O(\frac{\sqrt{n}}{n})\) ensures recursivity of the computable set. We also show that …

CombinatoricsRecursive setComputationComputabilityStructure (category theory)Graph (abstract data type)Continuum (set theory)Rose (topology)Projective planeMathematics
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CHARACTERS INDUCED FROM FULLY RAMIFIED SUBGROUPS

2001

Suppose that G is a finite π-separable group, let cf(G) be the space of complex class functions of G and let Irr(G) be the set of the irreducible complex characters of G. Let K be an arbitrary Hall...

CombinatoricsSet (abstract data type)Algebra and Number TheoryGroup (mathematics)Complex classSpace (mathematics)MathematicsCommunications in Algebra
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The Structure Group and the Permutation Group of a Set-Theoretic Solution of the Quantum Yang–Baxter Equation

2021

We describe the left brace structure of the structure group and the permutation group associated to an involutive, non-degenerate set-theoretic solution of the quantum YangBaxter equation by using the Cayley graph of its permutation group with respect to its natural generating system. We use our descriptions of the additions in both braces to obtain new properties of the structure and the permutation groups and to recover some known properties of these groups in a more transparent way.

CombinatoricsSet (abstract data type)Cayley graphYang–Baxter equationGroup (mathematics)Mathematics::Quantum AlgebraGeneral MathematicsStructure (category theory)Permutation groupMatemàticaQuantumMathematicsMediterranean Journal of Mathematics
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On periodic radical groups in which permutability is a transitive relation

2007

Abstract A group G is said to be a PT - group if permutability is a transitive relation in the set of all subgroups of G . Our purpose in this paper is to study PT -groups in the class of periodic radical groups satisfying min- p for all primes p .

CombinatoricsSet (abstract data type)Class (set theory)Transitive relationAlgebra and Number TheoryGroup (mathematics)MathematicsJournal of Pure and Applied Algebra
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On the Navarro–Willems conjecture for blocks of finite groups

2007

Abstract We prove that a set of characters of a finite group can only be the set of characters for principal blocks of the group at two different primes when the primes do not divide the group order. This confirms a conjecture of Navarro and Willems in the case of principal blocks.

CombinatoricsSet (abstract data type)Discrete mathematicsFinite groupAlgebra and Number TheoryConjectureGroup (mathematics)Group orderMathematicsJournal of Pure and Applied Algebra
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