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- W2950891337 abstract "Motivated by multiplication algorithms based on redundant number representations, we study representations of an integer $n$ as a sum $n=sum_k epsilon_k U_k$, where the digits $epsilon_k$ are taken from a finite alphabet $Sigma$ 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 $sum_k|epsilon_k|$ 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 order of magnitude of the number of representations of a given integer to the joint spectral radius of a certain set of matrices." @default.
- W2950891337 created "2019-06-27" @default.
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- W2950891337 date "2011-03-01" @default.
- W2950891337 modified "2023-09-25" @default.
- W2950891337 title "Redundancy of minimal weight expansions in Pisot bases" @default.
- W2950891337 hasPublicationYear "2011" @default.
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