相关论文: Balancedness of Arnoux-Rauzy and Brun words
The paper deals with balances and imbalances in Arnoux-Rauzy words. We provide sufficient conditions for $C$-balancedness, but our results indicate that even a characterization of 2-balanced Arnoux-Rauzy words on a 3-letter alphabet is not…
In the study of infinite words, various notions of balancedness provide quantitative measures for how regularly letters or factors occur, and they find applications in several areas of mathematics and theoretical computer science. In this…
This paper studies balancedness for infinite words and subshifts, both for letters and factors. Balancedness is a measure of disorder that amounts to strong convergence properties for frequencies. It measures the difference between the…
We construct an Arnoux-Rauzy word for which the set of all differences of two abelianized factors is equal to $\mathbb{Z}^3$. In particular, the imbalance of this word is infinite - and its Rauzy fractal is unbounded in all directions of…
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…
In the past few decades there has been a good deal of papers which are concerned with optimization problems in different areas of mathematics (along 0-1 words, finite or infinite) and which yield - sometimes quite unexpectedly - balanced…
We revisit the question of classification of balanced circular words and focus on the case of a ternary alphabet. We propose a $3$-dimensional generalisation of the discrete approximation representation of Christoffel words. By considering…
We consider the following problem. Let us fix a finite alphabet A; for any given d-uple of letter frequencies, how to construct an infinite word u over the alphabet A satisfying the following conditions: u has linear complexity function, u…
An infinite word generated by a substitution is rigid if all the substitutions which fix this word are powers of a same substitution. Sturmian words as well as characteristic Arnoux-Rauzy words are known to be rigid. In the present paper,…
A set of words, also called a language, is letter-balanced if the number of occurrences of each letter only depends on the length of the word, up to a constant. Similarly, a language is factor-balanced if the difference of the number of…
We prove that episturmian words and Arnoux-Rauzy sequences can be characterized using a local balance property. We also give a new characterization of epistandard words and show that the set of finite words that are not factors of an…
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…
The class of (eventually) dendric words generalizes well-known families such as the Arnoux-Rauzy words or the codings of interval exchanges. There are still many open questions about the link between dendricity and morphisms. In this paper,…
The non-repetitive complexity $nr\mathcal{C}_{\bf u}$ and the initial non-repetitive complexity $inr\mathcal{C}_{\bf u}$ are functions which reflect the structure of the infinite word ${\bf u}$ with respect to the repetitions of factors of…
We consider questions related to the structure of infinite words (over an integer alphabet) with bounded additive complexity, i.e., words with the property that the number of distinct sums exhibited by factors of the same length is bounded…
Frequency of letters in a symbolic sequence ${\bf u}$ over a finite alphabet is one of the basic characteristics of ${\bf u}$. The notion of $k$-balancedness captures the property that the number of any letter occurring in two arbitrary…
A celebrated theorem by Coven and Hedlund (1973) states that Sturmian words are characterized by their abelian complexity: they are precisely the infinite words with rationally independent letter frequencies and constant abelian complexity…
For $d\ge 1$, a word $w\in \{ 0,1\}^{\Z^d}$ is called balanced if there exists $M > 0$ such that for any two rectangles $R, R^{'}\subset\Z^d$ that are translates of each other, the number of occurrences of the symbol $1$ in $R$ and $R^{'}$…
We show that 3-braid links with given (non-zero) Alexander or Jones polynomial are finitely many, and can be effectively determined. We classify among closed 3-braids strongly quasipositive and fibered ones, and show that 3-braid links have…
Recently, a new characterization of Lyndon words that are also perfectly clustering was proposed by Lapointe and Reutenauer (2024). A word over a ternary alphabet {a,b,c} is called perfectly clustering Lyndon if and only if it is the…