Restricted Binary Strings and Generalized Fibonacci Numbers - Archive ouverte HAL Access content directly
Conference Papers Year : 2017

Restricted Binary Strings and Generalized Fibonacci Numbers

(1)
1

Abstract

We provide some interesting relations involving k-generalized Fibonacci numbers between the set $F_n^{(k)}$ of length n binary strings avoiding k of consecutive 0’s and the set of length n strings avoiding $k+1$ consecutive 0’s and 1’s with some more restriction on the first and last letter, via a simple bijection. In the special case $k=2$ a probably new interpretation of Fibonacci numbers is given.Moreover, we describe in a combinatorial way the relation between the strings of $F_n^{(k)}$ with an odd numbers of 1’s and the ones with an even number of 1’s.
Fichier principal
Vignette du fichier
447449_1_En_3_Chapter.pdf (301.53 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-01656354 , version 1 (05-12-2017)

Licence

Attribution - CC BY 4.0

Identifiers

Cite

Antonio Bernini. Restricted Binary Strings and Generalized Fibonacci Numbers. 23th International Workshop on Cellular Automata and Discrete Complex Systems (AUTOMATA), Jun 2017, Milan, Italy. pp.32-43, ⟨10.1007/978-3-319-58631-1_3⟩. ⟨hal-01656354⟩
63 View
127 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More