Restricted Binary Strings and Generalized Fibonacci Numbers

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.
Document type :
Conference papers
Complete list of metadatas

Cited literature [15 references]  Display  Hide  Download

https://hal.inria.fr/hal-01656354
Contributor : Hal Ifip <>
Submitted on : Tuesday, December 5, 2017 - 3:42:16 PM
Last modification on : Wednesday, December 6, 2017 - 10:47:38 AM

File

 Restricted access
To satisfy the distribution rights of the publisher, the document is embargoed until : 2020-01-01

Please log in to resquest access to the document

Licence


Distributed under a Creative Commons Attribution 4.0 International License

Identifiers

Citation

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⟩

Share

Metrics

Record views

78