On the Enumeration and Asymptotic Analysis of Fibonacci Compositions

Publication date: 27 October 2021

Abstract: We study Fibonacci compositions, which are compositions of natural numbers that only use Fibonacci numbers, in two different contexts. We first prove inequalities comparing the number of Fibonacci compositions to regular compositions where summands have a maximum possible value. Then, we consider asymptotic properties of Fibonacci compositions, comparing them to compositions whose terms come from positive linear recurrence sequences. Finally, we consider analogues of these results where we do not allow the use of a certain number of consecutive Fibonacci numbers starting from

F_{2} = 1

.

Has companion code repository: https://github.com/jmsiktar/fibbins

Mathematics Subject Classification ID

Asymptotic enumeration (05A16) Fibonacci and Lucas numbers and polynomials and generalizations (11B39)

This page was built for publication: On the Enumeration and Asymptotic Analysis of Fibonacci Compositions

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6381451)