10 citations · 24 across the 10 of their papers we have counts for
10 papers
Primes and composites in the determinant Hosoya triangle
Hsin-Yun Ching, Rigoberto Flórez, F. Luca +2
In this paper, we look at numbers of the form . These numbers are the entries of a triangular array called the \emph{determinant Hosoya tria…
Honeycombs in the Pascal triangle and beyond
Matthew Blair, Rigoberto Flórez, Antara Mukherjee
In this paper we present a geometric approach to discovering some known and some new identities using triangular arrays. Our main aim is to demonstrate how to use the geometric pat…
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 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…
Star of David and other patterns in the Hosoya-like polynomials triangles
Rigoberto Florez, Robinson A. Higuita, Antara Mukherjee
In this paper we first generalize the numerical recurrence relation given by Hosoya to polynomials. Using this generalization we construct a Hosoya-like triangle for polynomials, w…
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…
Isoperimetric Inequalities using Varopoulos Transport
Antara Mukherjee
The main results in this paper provide upper bounds of the second order Dehn functions for three-dimensional groups Nil and Sol. These upper bounds are obtained by using the Varopo…
Hyperbolic Groups Which Fiber in Infinitely Many Ways
TaraLee Mecham, Antara Mukherjee
We construct examples of free-by-cyclic hyperbolic groups which fiber in infinitely many ways over Z. The construction involves adding a specialized square 2-cell to a non-positive…