The Hybrid Numbers of Padovan and Some Identities
Milena Carolina dos Santos Mangueira, Renata Passos Machado Vieira, Francisco Régis Vieira Alves, Paula Catarino
Abstract
Abstract In this article, we will define Padovan’s hybrid numbers, based on the new noncommutative numbering system studied by Özdemir ([7]). Such a system that is a set involving complex, hyperbolic and dual numbers. In addition, Padovan’s hybrid numbers are created by combining this set, satisfying the relation ih = −hi = ɛ + i . Given this, some properties and identities are shown for these numbers, such as Binet’s formula, generating matrix, characteristic equation, norm, and generating function. In addition, these numbers are extended to the integer field and some identities are made.
Topics & Concepts
MathematicsNoncommutative geometryInteger (computer science)NumberingGenerating functionNorm (philosophy)Real numberSet (abstract data type)Fibonacci numberField (mathematics)Discrete mathematicsPure mathematicsAlgorithmComputer scienceLawPolitical scienceProgramming languageAdvanced Mathematical Theories and ApplicationsAdvanced Mathematical TheoriesMathematics and Applications