The number of valid factorizations of Fibonacci prefixes
Combinatorics
2019-01-08 v4 Formal Languages and Automata Theory
Abstract
We establish several recurrence relations and an explicit formula for V(n), the number of factorizations of the length-n prefix of the Fibonacci word into a (not necessarily strictly) decreasing sequence of standard Fibonacci words. In particular, we show that the sequence V(n) is the shuffle of the ceilings of two linear functions of n.
Cite
@article{arxiv.1806.09534,
title = {The number of valid factorizations of Fibonacci prefixes},
author = {Pierre Bonardo and Anna E. Frid and Jeffrey Shallit},
journal= {arXiv preprint arXiv:1806.09534},
year = {2019}
}
Comments
Version accepted to Theoretical Computer Science