Related papers: Critical exponents of infinite balanced words
We define a new class of languages of $\omega$-words, strictly extending $\omega$-regular languages. One way to present this new class is by a type of regular expressions. The new expressions are an extension of $\omega$-regular expressions…
We exhibit combinatorial results on Christoffel words and binary balanced words that are motivated by their geometric interpretation as approximations of digital segments. We give a closed formula for counting the exact number of balanced…
Meanders form a set of combinatorial problems concerned with the enumeration of self-avoiding loops crossing a line through a given number of points, $n$. Meanders are considered distinct up to any smooth deformation leaving the line fixed.…
We study the equality problem for infinite words obtained by iterating morphisms. In particular, we give a practical algorithm to decide whether or not two words generated by primitive morphisms are equal.
We consider Rote words, which are infinite binary words with factor complexity $2n$. We prove that the repetition threshold for this class is $5/2$. Our technique is purely computational, using the Walnut theorem prover and a new technique…
We find generating functions for the number of words avoiding certain patterns or sets of patterns on at most 2 distinct letters and determine which of them are equally avoided. We also find the exact number of words avoiding certain…
The critical point between varieties A and B of algebras is defined as the least cardinality of the semilattice of compact congruences of a member of A but of no member of B, if it exists. The study of critical points gives rise to a whole…
An infinite word is an infinite Lyndon word if it is smaller, with respect to the lexicographic order, than all its proper suffixes, or equivalently if it has infinitely many finite Lyndon words as prefixes. A characterization of binary…
In this paper, we investigate the expressive power and the algorithmic properties of weighted expressions, which define functions from finite words to integers. First, we consider a slight extension of an expression formalism, introduced by…
A word is square-free if it does not contain nonempty factors of the form $XX$. In 1906 Thue proved that there exist arbitrarily long square-free words over a $3$-letter alphabet. It was proved recently [7] that among these words there are…
In combinatorics on words, a classical topic of study is the number of specific patterns appearing in infinite sequences. For instance, many works have been dedicated to studying the so-called factor complexity of infinite sequences, which…
In this paper, we study the critical exponent of infinite words $\ubeta$ coding $\beta$-integers for $\beta$ being a~non-simple Parry number. In other words, we investigate the maximal consecutive repetitions of factors that occur in the…
For any integer $k>2$, the infinite $k$-bonacci word $W^{(k)}$, on the infinite alphabet is defined as the fixed point of the morphism $\varphi_k:\mathbb{N}\rightarrow \mathbb{N}^2 \cup \mathbb{N}$, where \begin{equation*} \varphi_k(ki+j) =…
Finite alphabets of at least three letters permit the construction of square-free words of infinite length. We show that the entropy density is strictly positive and derive reasonable lower and upper bounds. Finally, we present an…
We study critical bond percolation on periodic four-dimensional (4D) and five-dimensional (5D) hypercubes by Monte Carlo simulations. By classifying the occupied bonds into branches, junctions and non-bridges, we construct the whole, the…
Let $W$ be an infinite word over finite alphabet $A$. We get combinatorial criteria of existence of interval exchange transformations that generate the word W.
We characterize the clustering of a word under the Burrows-Wheeler transform in terms of the resolution of a bounded number of bispecial factors belonging to the language generated by all its powers. We use this criterion to compute, in…
We describe and implement an algorithm to find all post-critically finite (PCF) cubic polynomials defined over $\mathbb{Q}$, up to conjugacy over $\text{PGL}_2(\bar{\mathbb{Q}})$. We describe normal forms that classify equivalence classes…
An efficient, when compared to exhaustive enumeration, algorithm for computing the number of square-free words of length $n$ over the alphabet $\{a, b, c\}$ is presented.
We start by considering binary words containing the minimum possible numbers of squares and antisquares (where an antisquare is a word of the form $x \overline{x}$), and we completely classify which possibilities can occur. We consider…