Related papers: Dynamic and Programmatic Analysis of Fibonacci Wor…
The subword complexity of a finite word $w$ of length $N$ is a function which associates to each $n\le N$ the number of all distinct subwords of $w$ having the length $n$. We define the \emph{maximal complexity} C(w) as the maximum of the…
The precise analysis of the variance of the profile of a suffix tree has been a longstanding open problem. We analyze three regimes of the asymptotic growth of the variance of the profile of a suffix tree built from a randomly generated…
We study the asymptotics and fine-scale behavior of quantitative combinatorial measures of infinite words and related dynamical and algebraic structures. We construct infinite recurrent words $w$ whose complexity functions $p_w(n)$ are…
An upward (resp. downward) digitally convex word is a binary word that best approximates from below (resp. from above) an upward (resp. downward) convex curve in the plane. We study these words from the combinatorial point of view,…
We fully classify automatic sequences $a$ over a finite alphabet $\Omega$ with the property that each word over $\Omega$ appears is $a$ along an arithmetic progression. Using the terminology introduced by Avgustinovich, Fon-Der-Flaass and…
We construct automata with input(s) in Fibonacci representation (also known as Zeckendorf representation) recognizing some basic arithmetic relations and study their number of states. We also consider some basic operations on…
The complexity of a system description is a function of the entropy of its symbolic description. Prior to computing the entropy of the system description, an observation scale has to be assumed. In natural language texts, typical scales are…
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…
Any infinite uniformly recurrent word ${\bf u}$ can be written as concatenation of a finite number of return words to a chosen prefix $w$ of ${\bf u}$. Ordering of the return words to $w$ in this concatenation is coded by derivated word…
In this paper, we survey the rich theory of infinite episturmian words which generalize to any finite alphabet, in a rather resembling way, the well-known family of Sturmian words on two letters. After recalling definitions and basic…
The correlation dimension of natural language is measured by applying the Grassberger-Procaccia algorithm to high-dimensional sequences produced by a large-scale language model. This method, previously studied only in a Euclidean space, is…
Based on the combinatorial interpretation of the ordered Bell numbers, which count all the ordered partitions of the set $[n]=\{1,2,\dots,n\}$, we introduce the Fibonacci partition as a Fibonacci permutation of its blocks. Then we define…
Co-occurrence statistics based word embedding techniques have proved to be very useful in extracting the semantic and syntactic representation of words as low dimensional continuous vectors. In this work, we discovered that dictionary…
This paper proposes to use distributed representation of words (word embeddings) in cross-language textual similarity detection. The main contributions of this paper are the following: (a) we introduce new cross-language similarity…
A word is called closed if it has a prefix which is also its suffix and there is no internal occurrences of this prefix in the word. In this paper we study words that are rich in closed factors, i.e., which contain the maximal possible…
Bell and Shallit recently introduced the Lie complexity of an infinite word $s$ as the function counting for each length the number of conjugacy classes of words whose elements are all factors of $s$. They proved, using algebraic…
A beautiful theorem of Zeckendorf states that every integer can be written uniquely as a sum of non-consecutive Fibonacci numbers $\{F_n\}_{n=1}^{\infty}$. Lekkerkerker proved that the average number of summands for integers in $[F_n,…
We consider words $G_{i_1} \cdots G_{i_m}$ involving i.i.d. complex Ginibre matrices, and study tracial expressions of their eigenvalues and singular values. We show that the limit distribution of the squared singular values of every word…
Among the several findings deriving from the application of complex network formalism to the investigation of natural phenomena, the fact that linguistic constructions follow power laws presents special interest for its potential…
Let $\beta=\frac{1+\sqrt{5}}{2}$, $(a_n)_{n \in \mathbb{N}^+}$ be a non-uniform morphic sequence involving the infinite Fibonacci word and $(\delta(n))_{n \in \mathbb{N}^+}$ be a positive sequence such that for all positive integers $n$,…