Loyola University Chicago

Mathematics and Statistics

Mathematics and Statistics Colloquium (April 18)


Speaker: Rigoberto Florez (https://www.rigoflorez.com)

Affiliation: The Citadel, The Military College of South Carolina

When: April 18, 2024 from 4 to 5pm

Location: IES 110

Title: The strong divisibility property and the resultant of generalized Fibonacci polynomials

Abstract:  A second order polynomial sequence is of Fibonacci-type (Lucas-type) if its Binet formula has a structure similar to that for Fibonacci (Lucas) numbers. Those are known as generalized Fibonacci polynomials GFP. Some known examples are: Fibobacci Polynomials, Pell polynomials, Fermat polynomials, Chebyshev polynomials, Morgan-Voyce polynomials, Lucas polynomials, Pell-Lucas polynomials, Fermat-Lucas polynomials, Chebyshev polynomials, Vieta and Vieta-Lucas polynomials.
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 hold for every second order recursive sequence. We give a characterization of GFPs that satisfy the strong divisibility property. We also give formulas to evaluate the gcd of GFPs that do not satisfy the strong divisibility property.
In the end of the talk we talk about the irreducibility of GFP. Joint work with M. Diaz-Noguera, R. Higuita, M. Romero-Rojas, R. Ramirez, and J.C. Saunders.

Bio: Dr. Florez is an Associate Professor with a Ph.D. in Mathematics from Binghamton University (SUNY). His research is in combinatorics, especially graphs and algebraically representable matroids. He is also interested in elementary number theory and enumerative combinatorics. Rigo likes working research projects with undergraduate and graduate students. His students have presented their research in local and national conferences and they have won awards doing the same. He is one of the founders of Carolina Math Seminar.