Search results for "Constructive"

showing 10 items of 301 documents

Matchings in three Catalan lattices

2003

In this note we consider a series of lattices that are enumerated by the well-known Catalan numbers. For each of these lattices, we exhibit a matching in a constructive way.

Discrete mathematicsMathematics::CombinatoricsBinary treeHigh Energy Physics::LatticeApplied Mathematics010102 general mathematics0102 computer and information sciences16. Peace & justice01 natural sciencesConstructivelanguage.human_languageComputer Science ApplicationsCatalan numberCombinatoricsComputational Theory and Mathematics010201 computation theory & mathematicsLattice (order)[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]languageCatalan0101 mathematicsComputingMilieux_MISCELLANEOUSMathematics
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Dyck paths with a first return decomposition constrained by height

2018

International audience; We study the enumeration of Dyck paths having a first return decomposition with special properties based on a height constraint. We exhibit new restricted sets of Dyck paths counted by the Motzkin numbers, and we give a constructive bijection between these objects and Motzkin paths. As a byproduct, we provide a generating function for the number of Motzkin paths of height k with a flat (resp. with no flats) at the maximal height. (C) 2018 Elsevier B.V. All rights reserved.KeywordsKeyWords Plus:STATISTICS; STRINGS

Discrete mathematicsMathematics::CombinatoricsFirst return decompositionDyck and Motzkin pathsEnumerationHeightStatisticsGenerating function0102 computer and information sciences01 natural sciencesConstructiveTheoretical Computer ScienceConstraint (information theory)Combinatorics010104 statistics & probability010201 computation theory & mathematicsEnumerationBijectionDecomposition (computer science)Discrete Mathematics and CombinatoricsStrings0101 mathematics[MATH]Mathematics [math]MathematicsPeak
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Enumeration of Łukasiewicz paths modulo some patterns

2019

Abstract For any pattern α of length at most two, we enumerate equivalence classes of Łukasiewicz paths of length n ≥ 0 where two paths are equivalent whenever the occurrence positions of α are identical on these paths. As a byproduct, we give a constructive bijection between Motzkin paths and some equivalence classes of Łukasiewicz paths.

Discrete mathematicsMathematics::CombinatoricsModulo020206 networking & telecommunications0102 computer and information sciences02 engineering and technology[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]01 natural sciencesConstructiveTheoretical Computer ScienceCombinatoricsMathematics::Logic010201 computation theory & mathematics[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]0202 electrical engineering electronic engineering information engineeringEnumerationBijectionMathematics - CombinatoricsDiscrete Mathematics and CombinatoricsComputingMilieux_MISCELLANEOUSMathematics
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A new Euler–Mahonian constructive bijection

2011

AbstractUsing generating functions, MacMahon proved in 1916 the remarkable fact that the major index has the same distribution as the inversion number for multiset permutations, and in 1968 Foata gave a constructive bijection proving MacMahon’s result. Since then, many refinements have been derived, consisting of adding new constraints or new statistics.Here we give a new simple constructive bijection between the set of permutations with a given number of inversions and those with a given major index. We introduce a new statistic, mix, related to the Lehmer code, and using our new bijection we show that the bistatistic (mix,INV) is Euler–Mahonian. Finally, we introduce the McMahon code for …

Discrete mathematicsMultisetMathematics::CombinatoricsApplied MathematicsMajor indexMajor indexConstructiveCombinatoricssymbols.namesakeConstructive bijectionLehmer codeBijectionEuler's formulasymbolsInversion numberDiscrete Mathematics and CombinatoricsPermutation (bi)statisticStatisticMathematicsDiscrete Applied Mathematics
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General inductive inference types based on linearly-ordered sets

1996

In this paper, we reconsider the definitions of procrastinating learning machines. In the original definition of Freivalds and Smith [FS93], constructive ordinals are used to bound mindchanges. We investigate the possibility of using arbitrary linearly ordered sets to bound mindchanges in a similar way. It turns out that using certain ordered sets it is possible to define inductive inference types more general than the previously known ones. We investigate properties of the new inductive inference types and compare them to other types.

Discrete mathematicsOrdered setRecursive functionsInductive reasoningConstructiveMaximal elementMathematics
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Amount of Nonconstructivity in Finite Automata

2009

When D. Hilbert used nonconstructive methods in his famous paper on invariants (1888), P.Gordan tried to prevent the publication of this paper considering these methods as non-mathematical. L. E. J. Brouwer in the early twentieth century initiated intuitionist movement in mathematics. His slogan was "nonconstructive arguments have no value for mathematics". However, P. Erdos got many exciting results in discrete mathematics by nonconstructive methods. It is widely believed that these results either cannot be proved by constructive methods or the proofs would have been prohibitively complicated. R.Freivalds [7] showed that nonconstructive methods in coding theory are related to the notion of…

Discrete mathematicsProbabilistic methodDeterministic finite automatonKolmogorov complexityIntuitionismLimit (mathematics)Mathematical proofConstructiveMethod of conditional probabilitiesMathematics
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Contenuti e learning outcomes: una proposta per gli insegnamenti del Corso di Specializzazione sul sostegno

2020

Il lavoro nell’ottica del monitoraggio e del miglioramento ai fini della progettazione delle attività future del Corso di Specializzazione per le Attività di Sostegno (D.M. 30 settembre 2011), si colloca in seno all’attuale dibattito sulla ricerca di indicatori specifici e di strumenti condivisi per valutare e migliorare i risultati della didattica universitaria in questo ambito. L’individuazione dei contenuti core nei Corsi di Specializzazione rappresenta un elemento chiave per la progettazione e la formazione dei futuri docenti di sostegno. L’articolo presenta l’impostazione metodologica di un processo di ricerca messo in atto presso l’Università degli Studi di Palermo nell’a.a. 2018/19, …

Dublin descriptorcontenuti coreallineamento costruttivoconstructive alignmentsupport teacherDescrittori di DublinoPedagogical Content Knowledgeinsegnanti di sostegnocore contentSettore M-PED/03 - Didattica E Pedagogia Speciale
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General Diagnosis and Medical Evaluation

2019

Current literature does not contribute to a high level of evidence regarding possible indications for immediate loading. A great variety of exclusion criteria for immediate loading of dental implants are used in different studies. However, the reported criteria are similar to those chosen for conventional loading of dental implants. Despite its several clinical advantages, the immediate loading protocol should be performed respecting a rigorous preliminary diagnostic algorithm. Primary indication for immediate implant loading is certainly patients’ desire to reduce the overall treatment time. Additionally, several psychological factors, related to the preservation of functional and esthetic…

EdentulismReconstructive surgerymedicine.medical_specialtybusiness.industryDentistryMedical evaluationEvidence-based medicinemedicine.diseaseOral hygieneImmediate loadingMedicineImplantbusinessContraindication
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Numerical analysis of a new cross-flow type hydraulic turbine for high head and low flow rate

2021

Cross-flow turbines have recently been proposed for energy recovery in aqueducts when the outlet pressure is greater than zero, owing to their constructive simplicity and good efficiency within a large range of flow rates and head drops. In the case of high head drop (higher than 150 m) and relatively small discharge (lower than 0.2 m3/s), the traditional design of these turbines leads to very small widths of the nozzle and the runner; as a consequence, friction losses grow dramatically and efficiency drops down to very low values. Standard Pelton turbines require zero outlet pressure and cannot be used as alternatives. A new counter-pressure hydraulic turbine for high head and low flow rat…

Energy recoveryGeneral Computer ScienceNumerical analysisenergy recoveryMechanicsEngineering (General). Civil engineering (General)ConstructiveVolumetric flow rateSettore ICAR/01 - Idraulicabanki–michell turbinecross-flow turbineModeling and SimulationSimplicity (photography)water distribution networkHead (vessel)Cross-flow turbineTA1-2040micro-hydropowerMicro-hydropower energy recovery cross-flow turbine water distribution network Banki–Michell turbineHydraulic turbinesMathematicsEngineering Applications of Computational Fluid Mechanics
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Designing an Innovative Face-Milling Cutter

2013

The paper consists in a research in the design of an innovative face-milling cutter, in terms of product lifecycle management (PLM), with the help from creative design methods, such as TRIZ. The model of the lifecycle management of the cutting tools was presented, emphasizing the functional analysis and creative design phase. Based on this analysis, a new constructive variant of the milling cutter was designed and simulated with finite element method, highlighting its advantages compared with classic construction variants.

Engineering drawingEngineeringbusiness.industryModal analysisComputerApplications_COMPUTERSINOTHERSYSTEMSGeneral MedicineConstructiveFinite element methodManufacturing engineeringlaw.inventionApplication lifecycle managementProduct lifecyclelawFace (geometry)Milling cutterTRIZbusinessApplied Mechanics and Materials
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