Related papers: Asymptotic bit frequency in Fibonacci words
This paper concerns a specific class of strict standard episturmian words whose directive words resemble those of characteristic Sturmian words. In particular, we explicitly determine all integer powers occurring in such infinite words,…
Given k>1, let a_n be the sequence defined by the recurrence a_n=c_1a_{n-1}+c_2a_{n-2}+...+c_ka_{n-k} for n>=k, with initial values a_0=a_1=...=a_{k-2}=0 and a_{k-1}= 1. We show under a couple of assumptions concerning the constants c_i…
We study Piatetski-Shapiro sequences $(\lfloor n^c\rfloor)_n$ modulo m, for non-integer $c >1$ and positive $m$, and we are particularly interested in subword occurrences in those sequences. We prove that each block $\in\{0,1\}^k$ of length…
We show that the set of the numbers that are the sum of a prime and a Fibonacci number has positive lower asymptotic density.
We prove that a random word of length $n$ over a $k$-ary fixed alphabet contains, on expectation, $\Theta(\sqrt{n})$ distinct palindromic factors. We study this number of factors, $E(n,k)$, in detail, showing that the limit…
This paper is about counting the number of distinct (scattered) subwords occurring in a given word. More precisely, we consider the generalization of the Pascal triangle to binomial coefficients of words and the sequence $(S(n))_{n\ge 0}$…
The Fibonacci word is the fixed point beginning with the letter $a$ of morphism $\sigma(a)=ab$, $\sigma(b)=a$ defined over the alphabet $\{a,b\}$. In this paper, we get explicit expression of the number of distinct fractional powers in each…
Let a word be a sequence of $n$ i.i.d. integer random variables. The perimeter $P$ of the word is the number of edges of the word, seen as a polyomino. In this paper, we present a probabilistic approach to the computation of the moments of…
Morphic words are letter-to-letter images of fixed points $x$ of morphisms on finite alphabets. There are situations where these letter-to-letter maps do not occur naturally, but have to be replaced by a morphism. We call this a decoration…
This paper proposes an alternative language for expressing results of the algorithmic theory of randomness. The language is more precise in that it does not involve unspecified additive or multiplicative constants, making mathematical…
We study the notion of an asymptotically automatic sequence, which generalises the notion of an automatic sequence. While $k$-automatic sequences are characterised by finiteness of $k$-kernels, the $k$-kernels of asymptotically…
In this paper we study the enumeration and the construction, according to the number of ones, of particular binary words avoiding a fixed pattern. The growth of such words can be described by particular jumping and marked succession rules.…
A net occurrence of a repeated string in a text is an occurrence with unique left and right extensions, and the net frequency of the string is the number of its net occurrences in the text. Originally introduced for applications in Natural…
We determine the maximal length of the period of a periodic word defined by $n$ restrictions. It happens to be the corresponding Fibonacci number.
The rate of occurrence of words is not uniform but varies from document to document. Despite this observation, parameters for conventional n-gram language models are usually derived using the assumption of a constant word rate. In this…
A reformulation of the path length of binary search trees is given in terms of permutations, allowing to extend the definition to the instance of words, where the letters are obtained by independent geometric random variables (with…
We consider the possible visits to visible points of a random walker moving up and right in the integer lattice (with probability $\alpha$ and $1-\alpha$, respectively) and starting from the origin. We show that, almost surely, the…
In this paper, we analyze the density of the Fibonacci word and its derived forms by examining the morphisms associated with each. It offers a comparative analysis of the density of Fibonacci numbers alongside other words derived from…
We determine the asymptotic proportion of minimal automata, within n-state accessible deterministic complete automata over a k-letter alphabet, with the uniform distribution over the possible transition structures, and a binomial…
We generalize the quantum random walk protocol for a particle in a one-dimensional chain, by using several types of biased quantum coins, arranged in aperiodic sequences, in a manner that leads to a rich variety of possible wave function…