Search results for "Crete"

showing 10 items of 2495 documents

Some Generalizations of a Simion Schmidt Bijection

2007

In 1985, Simion and Schmidt gave a constructive bijection φ from the set of all length (n-1) binary strings having no two consecutive 1s to the set of all length n permutations avoiding all patterns in {123,132,213}. In this paper, we generalize φ to an injective function from {0,1}n-1 to the set Sn of all length n permutations and derive from it four bijections φ : P →Q where P⊆{0,1}n-1 and Q ⊂ Sn. The domains are sets of restricted binary strings and the codomains are sets of pattern-avoiding permutations. As a particular case we retrieve the original Simion–Schmidt bijection. We also show that the bijections obtained are actually combinatorial isomorphisms, i.e. closeness-preserving bije…

Set (abstract data type)Discrete mathematicsGray codeCombinatoricsMathematics::CombinatoricsGeneral Computer ScienceCodomainBijectionIsomorphismBijection injection and surjectionConstructiveInjective functionMathematicsThe Computer Journal
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Closedness Properties in EX-Identification of Recursive Functions

1998

In this paper we investigate in which cases unions of identifiable classes of recursive functions are also necessarily identifiable. We consider identification in the limit with bounds on mindchanges and anomalies. Though not closed under the set union, these identification types still have features resembling closedness. For each of them we find such n that 1) if every union of n - 1 classes out of U1;, . . ., Un is identifiable, so is the union of all n classes; 2) there are such classes U1;, . . ., Un-1 that every union of n-2 classes out of them is identifiable, while the union of n - 1 classes is not. We show that by finding these n we can distinguish which requirements put on the iden…

Set (abstract data type)Discrete mathematicsIdentification (information)Limit (category theory)AlgorithmicsInferenceIdentifiabilityInductive reasoningBoolean functionMathematics
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Unions of identifiable families of languages

1996

This paper deals with the satisfiability of requirements put on the identifiability of unions of language families. We consider identification in the limit from a text with bounds on mindchanges and anomalies. We show that, though these identification types are not closed under the set union, some of them still have features that resemble closedness. To formalize this, we generalize the notion of closedness. Then by establishing “how closed” these identification types are we solve the satisfiability problem.

Set (abstract data type)Discrete mathematicsIdentification (information)Limit (category theory)IdentifiabilityLanguage familyInductive reasoningBoolean satisfiability problemMathematical economicsSatisfiabilityMathematics
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Bernstein sets andκ-coverings

2010

䅢stract. In this paper we study a notion of a �-covering in connection with Bernstein sets and other types of nonmeasurability. Our results correspond to those obtained by Muthuvel in [7] and Nowik in [8]. We consider also other types of coverings. 1. Definitions and notation In 1993 Car汳on 楮 h楳 paper 嬳] 楮troduced a not楯n of �-cover楮gs and used 楴 for 楮vest楧at楮g whether some 楤ea汳 are or are not �-trans污tab汥. Later on �-cover楮gs were stud楥d by other authors, e⹧. Muthuvel (cf. [7 崩 and Now楫 (cf. 嬸崬 嬹崩. In th楳 paper we present new resu汴s on �-cover楮gs 楮 connect楯n w楴h Bernste楮 sets. We a汳o 楮troduce two natural genera汩zat楯ns of the not楯n of �-cover楮gs, name汹 �-S-cover楮gs and �-I-cover楮gs. We use …

Set (abstract data type)Discrete mathematicsLogicNotationMathematicsReal numberConnection (mathematics)MLQ
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The set of conjugacy class sizes of a finite group does not determine its solvability

2014

Abstract We find a pair of groups, one solvable and the other non-solvable, with the same set of conjugacy class sizes.

Set (abstract data type)Discrete mathematicsMathematics::Group TheoryFinite groupTheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGESTheoryofComputation_COMPUTATIONBYABSTRACTDEVICESAlgebra and Number TheoryConjugacy classTheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITYComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONMathematicsofComputing_DISCRETEMATHEMATICSMathematicsJournal of Algebra
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Maximal subgroups and formations

1989

Abstract We define, in each finite group G , some subgroups of Frattini-type in relation with a saturated formation and with a set of primes and study their properties, especially their influence in the structure of G .

Set (abstract data type)Discrete mathematicsMathematics::Group TheoryPure mathematicsFinite groupMaximal subgroupAlgebra and Number TheoryRelation (database)Structure (category theory)CosetMathematicsJournal of Pure and Applied Algebra
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Nilpotent and perfect groups with the same set of character degrees

2014

We find a pair of finite groups, one nilpotent and the other perfect, with the same set of character degrees.

Set (abstract data type)Discrete mathematicsNilpotentPure mathematicsAlgebra and Number TheoryCharacter (mathematics)Applied MathematicsNilpotent groupUnipotentCentral seriesMathematicsJournal of Algebra and Its Applications
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Attracting sets in a deterministic discrete traffic model

2001

The fundamental diagram of the Nagel-Schreckenberg traffic model is derived analytically for the deterministic case using methods and concepts from nonlinear dynamics. It is shown that the possible states of the long-term behaviour form a globally attractive subset which can be well characterized. This attractive set of states is composed of coexisting attractors. The attractor concept is applied to a slow-to-start extension of the model. For this example it is shown that the attractive set consists of coexisting attractors with different macroscopic properties, that can be determined analytically.

Set (abstract data type)Discrete mathematicsNonlinear systemAttractorDiagramTraffic modelGeneral Physics and AstronomyApplied mathematicsStatistical and Nonlinear PhysicsExtension (predicate logic)Mathematical PhysicsMathematicsJournal of Physics A: Mathematical and General
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Reducing Local Alphabet Size in Recognizable Picture Languages

2021

A recognizable picture language is defined as the projection of a local picture language defined by a set of two-by-two tiles, i.e. by a strictly-locally-testable (SLT) language of order 2. The family of recognizable picture languages is also defined, using larger k by k tiles, \(k>2\), by the projection of the corresponding SLT language. A basic measure of the descriptive complexity of a picture language is given by the size of the SLT alphabet using two-by-two tiles, more precisely by the so-called alphabetic ratio of sizes: SLT-alphabet/picture-alphabet. We study how the alphabetic ratio changes moving from two to larger tile sizes, and we obtain the following result: any recognizable pi…

Set (abstract data type)Discrete mathematicsProjection (mathematics)Property (programming)Order (ring theory)AlphabetDescriptive complexity theoryPicture languageMeasure (mathematics)Mathematics
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On WQO Property for Different Quasi Orderings of the Set of Permutations

2013

The property of certain sets being well quasi ordered (WQO) has several useful applications in computer science – it can be used to prove the existence of efficient algorithms and also in certain cases to prove that a specific algorithm terminates.

Set (abstract data type)Discrete mathematicsProperty (philosophy)Efficient algorithmComputer scienceComputerApplications_COMPUTERSINOTHERSYSTEMS
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