Matrix analysis
An introduction to symbolic dynamics and coding
An introduction to symbolic dynamics and coding
Modern computer algebra
Linear Numeration Systems, Theta-Developments and Finite Automata
STACS '89 Proceedings of the 6th Annual Symposium on Theoretical Aspects of Computer Science
Distribution results for low-weight binary representations for pairs of integers
Theoretical Computer Science - Combinatorics of the discrete plane and tilings
On the Number of Optimal Base 2 Representations of Integers
Designs, Codes and Cryptography
Elements of Automata Theory
| Hi-index | 5.23 |
Motivated by multiplication algorithms based on redundant number representations, we study representations of an integer n as a sum n=@?"k@e"kU"k, where the digits @e"k are taken from a finite alphabet @S and (U"k)"k is a linear recurrent sequence of Pisot type with U"0=1. The most prominent example of a base sequence (U"k)"k is the sequence of Fibonacci numbers. We prove that the representations of minimal weight @?"k|@e"k| are recognised by a finite automaton and obtain an asymptotic formula for the average number of representations of minimal weight. Furthermore, we relate the maximal number of representations of a given integer to the joint spectral radius of a certain set of matrices.