### Words and repeated factors.

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We introduce the notion of a $k$-synchronized sequence, where $k$ is an integer larger than 1. Roughly speaking, a sequence of natural numbers is said to be $k$-synchronized if its graph is represented, in base $k$, by a right synchronized rational relation. This is an intermediate notion between $k$-automatic and $k$-regular sequences. Indeed, we show that the class of $k$-automatic sequences is equal to the class of bounded $k$-synchronized sequences and that the class of $k$-synchronized sequences is strictly...

We introduce the notion of a -synchronized sequence, where is an integer larger than 1. Roughly speaking, a sequence of natural numbers is said to be -synchronized if its graph is represented, in base , by a right synchronized rational relation. This is an intermediate notion between -automatic and -regular sequences. Indeed, we show that the class of -automatic sequences is equal to the class of bounded -synchronized sequences and that the class of -synchronized sequences is strictly...

The characteristic parameters ${K}_{w}$ and ${R}_{w}$ of a word $w$ over a finite alphabet are defined as follows: ${K}_{w}$ is the minimal natural number such that $w$ has no repeated suffix of length ${K}_{w}$ and ${R}_{w}$ is the minimal natural number such that $w$ has no right special factor of length ${R}_{w}$. In a previous paper, published on this journal, we have studied the distributions of these parameters, as well as the distribution of the maximal length of a repetition, among the words of each length on a given alphabet. In this paper...

For any finite word $w$ on a finite alphabet, we consider the basic parameters ${R}_{w}$ and ${K}_{w}$ of $w$ defined as follows: ${R}_{w}$ is the minimal natural number for which $w$ has no right special factor of length ${R}_{w}$ and ${K}_{w}$ is the minimal natural number for which $w$ has no repeated suffix of length ${K}_{w}$. In this paper we study the distributions of these parameters, here called characteristic parameters, among the words of each length on a fixed alphabet.

For any finite word on a finite alphabet, we consider the basic parameters and of defined as follows: is the minimal natural number for which has no right special factor of length and is the minimal natural number for which has no repeated suffix of length . In this paper we study the distributions of these parameters, here called characteristic parameters, among the words of each length...

The characteristic parameters and of a word over a finite alphabet are defined as follows: is the minimal natural number such that has no repeated suffix of length and is the minimal natural number such that has no right special factor of length . In a previous paper, published on this journal, we have studied the distributions of these parameters, as well as the distribution of the maximal...

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