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Conference Papers Year : 2017

## Restricted Binary Strings and Generalized Fibonacci Numbers

(1)
1
Antonio Bernini
• Function : Author
• PersonId : 1024519

#### 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.

#### Domains

Computer Science [cs]

### Dates and versions

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

### Identifiers

• HAL Id : hal-01656354 , version 1
• DOI :

### 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⟩

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