10 citations · 21 across the 10 of their papers we have counts for
10 papers
Zeros and Orthogonality of generalized Fibonacci polynomials
Cristian F. Coletti, Rigoberto Flórez, Robinson A. Higuita +1
This paper analyzes the concept of orthogonality in second-order polynomial sequences that have Binet formula similar to that of the Fibonacci and Lucas numbers, referred to as Gen…
Restricted Dyck Paths on Valleys Sequence
Rigoberto Flórez, Toufik Mansour, José L. Ramírez +2
In this paper we study a subfamily of a classic lattice path, the \emph{Dyck paths}, called \emph{restricted -Dyck} paths, in short -Dyck. A valley of a Dyck path is a lo…
Fibonacci identities from Jordan Identities
Santiago Alzate, Oscar Correa, Rigoberto Flórez
In this paper, we connect two well established theories, the Fibonacci numbers and the Jordan algebras. We give a series of matrices, from literature, used to obtain recurrence rel…
Families of Integral Cographs within a Triangular Arrays
Hsin-Yun Ching, Rigoberto Flórez, Antara Mukherjee
The \emph{determinant Hosoya triangle}, is a triangular array where the entries are the determinants of two-by-two Fibonacci matrices. The determinant Hosoya triangle g…
Matrices in the Hosoya triangle
Matthew Blair, Rigoberto Flórez, Antara Mukherjee
In this paper we use well-known results from linear algebra as tools to explore some properties of products of Fibonacci numbers. Specifically, we explore the behavior of the eigen…
The resultant, the discriminant, and the derivative of generalized Fibonacci polynomials
Rigoberto Flórez, Robinson Higuita, Alexander Ramírez
A second order polynomial sequence is of \emph{Fibonacci-type} (\emph{Lucas-type}) if its Binet formula has a structure similar to that for Fibonacci (Lucas) numbers. Known example…
The Geometry of some Fibonacci Identities in the Hosoya Triangle
Rigoberto Flórez, Robinson A. Higuita, Antara Mukherjee
The \emph{Hosoya triangle} is a triangular array where every entry is a product of two Fibonacci numbers. We use the geometry of this triangle to find new identities related to Fib…
The Projective Planarity Question for Matroids of -Nets and Biased Graphs
Rigoberto Flórez, Thomas Zaslavsky
A biased graph is a graph with a class of selected circles ("cycles", "circuits"), called "balanced", such that no theta subgraph contains exactly two balanced circles. A biased gr…
Identities for the generalized Fibonacci polynomial
Rigoberto Flórez, Nathan McAnally, Antara Mukherjee
A second order polynomial sequence is of Fibonacci type (Lucas type) if its Binet formula is similar in structure to the Binet formula for the Fibonacci (Lucas) numbers. In this pa…
Characterization of the strong divisibility property for generalized Fibonacci polynomials
Rigoberto Flórez, Robinson A. Higuita, Antara Mukherjee
It is known that the greatest common divisor of two Fibonacci numbers is again a Fibonacci number. It is called the strong divisibility property. However, this property does not ho…