相关论文: Quasi-Sturmian colorings on regular trees
In this article, we study subword complexity of colorings of regular trees. We characterize colorings of bounded subword complexity and study Sturmian colorings, which are colorings of minimal unbounded subword complexity. We classify…
Factor complexity $b_\phi(n)$ for a vertex coloring $\phi$ of a regular tree is the number of colored $n$-balls up to color-preserving automorphisms. Sturmian colorings are colorings of minimal unbounded factor complexity $b_\phi(n) = n+2$.…
In this paper, we consider infinite words that arise as fixed points of primitive substitutions on a finite alphabet and finite colorings of their factors. Any such infinite word exhibits a "hierarchal structure" that will allow us to…
Sturmian words are infinite binary words with many equivalent definitions: They have a minimal factor complexity among all aperiodic sequences; they are balanced sequences (the labels 0 and 1 are as evenly distributed as possible) and they…
The set of finite words over a well-quasi-ordered set is itself well-quasi-ordered. This seminal result by Higman is a cornerstone of the theory of well-quasi-orderings and has found numerous applications in computer science. However, this…
Recently the second two authors characterized quasiperiodic Sturmian words, proving that a Sturmian word is non-quasiperiodic if and only if it is an infinite Lyndon word. Here we extend this study to episturmian words (a natural…
We consider the following open question in the spirit of Ramsey theory: Given an aperiodic infinite word $w$, does there exist a finite coloring of its factors such that no factorization of $w$ is monochromatic? We show that such a coloring…
In this paper, we characterize by lexicographic order all finite Sturmian and episturmian words, i.e., all (finite) factors of such infinite words. Consequently, we obtain a characterization of infinite episturmian words in a "wide sense"…
The notion of almost periodicity nontrivially generalizes the notion of periodicity. Strongly almost periodic sequences (=uniformly recurrent infinite words) first appeared in the field of symbolic dynamics, but then turned out to be…
The complexity of an infinite word can be measured in several ways, the two most common measures being the subword complexity and the abelian complexity. In 2015, Rigo and Salimov introduced a family of intermediate complexities indexed by…
Given a finite coloring (or finite partition) of the free semigroup $A^+$ over a set $A$, we consider various types of monochromatic factorizations of right sided infinite words $x\in A^\omega$. Some stronger versions of the usual notion of…
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…
We introduce a new geometric approach to Sturmian words by means of a mapping that associates certain lines in the n x n -grid and sets of finite Sturmian words of length n. Using this mapping, we give new proofs of the formulas enumerating…
Words are sequences of letters over a finite alphabet. We study two intimately related topics for this object: quasi-randomness and limit theory. With respect to the first topic we investigate the notion of uniform distribution of letters…
We study the notion of quasiperiodicity, in the sense of "coverability", for biinfinite words. All previous work about quasiperiodicity focused on right infinite words, but the passage to the biinfinite case could help to prove stronger…
This article considers some affine algebraic varieties attached to finite trees and closely related to cluster algebras. Their definition involves a canonical coloring of vertices of trees into three colors. These varieties are proved to be…
This paper studies the structure of graphs with given tree-width and excluding a fixed complete bipartite subgraph, which generalises the bounded degree setting. We give a new structural description of such graphs in terms of so-called…
In this short article, we study factor colorings of aperiodic linearly recurrent infinite words. We show that there always exists a coloring which does not admit a monochromatic factorization of the word into factors of increasing lengths.
Return words constitute a powerful tool for studying symbolic dynamical systems. They may be regarded as a discrete analogue of the first return map in dynamical systems. In this paper we investigate two abelian variants of the notion of…
String attractors are a combinatorial tool coming from the field of data compression. It is a set of positions within a word which intersects an occurrence of every factor. While one-sided infinite words admitting a finite string attractor…