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...
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 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 length of a repetition, among the words of each length on a given alphabet. In this paper...
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 on a fixed alphabet.
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...
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...
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