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  • Author: José L. Ramírez x
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José L. Ramírez

Abstract

In this paper, we define the k-Fibonacci and the k-Lucas quaternions. We investigate the generating functions and Binet formulas for these quaternions. In addition, we derive some sums formulas and identities such as Cassini’s identity.

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Jósé L. Ramírez and Gustavo N. Rubiano

Abstract

In this paper we define the k-Fibonacci words in analogy with the definition of the k-Fibonacci numbers. We study their properties and we associate to this family of words a family of curves with interesting patterns.

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Takao Komatsu and José L. Ramírez

Abstract

We study some properties of restricted and associated Fubini numbers. In particular, they have the natural extensions of the original Fubini numbers in the sense of determinants. We also introduce modified Bernoulli and Cauchy numbers and study characteristic properties.