Abstract
There is a family of vector bundles over the moduli space of stable curves that, while first appearing in theoretical physics, has been an active topic of study for algebraic geometers since the 1990s. By computing the rank of the exceptional Lie algebra g2 case of these bundles in three different ways, a family of summation formulas for Fibonacci numbers in terms of the golden ratio is derived.
Highlights
The purpose of this note is to establish the following elementary summation formulas involving the famous Fibonacci numbers: Theorem 1
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations
One of the most significant properties of these bundles is their recursive structure reflecting the boundary stratification of M g,n. This property, known as factorization, was cleverly used by Mukhopadhyay to compute the rank of the g2, level 1, case of these bundles and the formula he obtained [12] is the middle expression in Equation (1) involving the golden ratio; by using factorization in two different ways, we obtain the two Fibonacci summation expressions in that equation
Summary
The purpose of this note is to establish the following elementary summation formulas involving the famous Fibonacci numbers: Theorem 1. One of the most significant properties of these bundles is their recursive structure reflecting the boundary stratification of M g,n This property, known as factorization, was cleverly used by Mukhopadhyay to compute the rank of the g2 , level 1, case of these bundles and the formula he obtained [12] is the middle expression in Equation (1) involving the golden ratio; by using factorization in two different ways, we obtain the two Fibonacci summation expressions in that equation. The details of this assertion are the content of this paper.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
