Related papers: Abelian returns in Sturmian words

The abelian critical exponent of an infinite word $w$ is defined as the maximum ratio between the exponent and the period of an abelian power occurring in $w$. It was shown by Fici et al. that the set of finite abelian critical exponents of…

As suggested by Currie, we apply the probabilistic method to problems regarding pattern avoidance. Using techniques from analytic combinatorics, we calculate asymptotic pattern occurrence statistics and use them in conjunction with the…

We prove new results concerning the relation between bifix codes, episturmian words and subgroups offree groups. We study bifix codes in factorial sets of words. We generalize most properties of ordinary maximal bifix codes to bifix codes…

An infinite word, which is aperiodic and codes the orbit of a transformation of the exchange of three intervals is called 3iet word. Such a word is thus a natural generalization of a sturmian word to a word over 3-letter alphabet. A…

The avoidability, or unavoidability of patterns in words over finite alphabets has been studied extensively. A word (pattern) over a finite set is said to be unavoidable if, for all but finitely many words, there exists a morphism mapping…

Recursive relational specifications are commonly used to describe the computational structure of formal systems. Recent research in proof theory has identified two features that facilitate direct, logic-based reasoning about such…

We introduce a class of sets of words which is a natural common generalization of Sturmian sets and of interval exchange sets. This class of sets consists of the uniformly recurrent tree sets, where the tree sets are defined by a condition…

We give a necessary and sufficient condition for a morphism between recollements of abelian categories to be an equivalence.

We present a framework which allows a uniform approach to the recently introduced concept of pseudo-repetitions on words in the morphic case. This framework is at the same time more general and simpler. We introduce the concept of a…

We introduce new avoidability problems for words by considering equivalence relations, k-abelian equivalences, which lie properly in between equality and commutative equality, i.e. abelian equality. For two k-abelian equivalent words the…

Let $R_\alpha$ be an irrational rotation of the circle, and code the orbit of any point $x$ by whether $R_\alpha^i(x)$ belongs to $[0,\alpha)$ or $[\alpha,1)$ -- this produces a Sturmian sequence. A point is undetermined at step $j$ if its…

A vocabulary is a list of words designating subsets from a grand set X. We model a vocabulary as a partition of X and study the aggregation of individual vocabularies into a collective one. We characterize aggregation rules when X is…

The paper gives a simple algebraic description, and background justification, for the Bowley Ratio, the relative returns to labour and capital, in a simple economy.

We show that the permutation complexity of the image of a Sturmian word by a binary marked morphism is $n+k$ for some constant $k$ and all lengths $n$ sufficiently large.

We define a fragment of monadic infinitary second-order logic corresponding to an abstract separation property. We use this to define the concept of a separation subclass. We use model theoretic techniques and games to show that separation…

Let $F$ be a free non-abelian group. We show that for any group word $w$ the set $w[F]$ of all values of $w$ in $F$ is rational in $F$ if and only if $w[F] = 1$ or $w[F] = F.$ We generalize this to a wide class of free products of groups.

The goal of this paper is to present an algebraic approach to the basic results of the theory of linear recurrence relations. This approach is based on the ideas from the theory of representations of one endomorphisms (a special case of…

Arabic morphology encapsulates many valuable features such as word root. Arabic roots are being utilized for many tasks; the process of extracting a word root is referred to as stemming. Stemming is an essential part of most Natural…

Let $w$ be an infinite word on an alphabet $A$. We denote by $(n_i)_{i \geq 1}$ the increasing sequence (assumed to be infinite) of all lengths of palindrome prefixes of $w$. In this text, we give an explicit construction of all words $w$…

We find the two-variables generating function for the statistic which counts the number of variations in a word bounded by $1$. Thus, we refine and extend previous results concerning staircase words, which are words in which the variation…