相关论文: Density dichotomy in random words
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…
A graph $G=(V,E)$ is word-representable if and only if there exists a word $w$ over the alphabet $V$ such that letters $x$ and $y$, $x\neq y$, alternate in $w$ if and only if $xy\in E$. A split graph is a graph in which the vertices can be…
Quantitative linguistics has provided us with a number of empirical laws that characterise the evolution of languages and competition amongst them. In terms of language usage, one of the most influential results is Zipf's law of word…
We consider a measure of similarity for infinite words that generalizes the notion of asymptotic or natural density of subsets of natural numbers from number theory. We show that every overlap-free infinite binary word, other than the…
The complexity function of an infinite word $w$ on a finite alphabet $A$ is the sequence counting, for each non-negative $n$, the number of words of length $n$ on the alphabet $A$ that are factors of the infinite word $w$. For any given…
In this paper we investigate local to global phenomena for a new family of complexity functions of infinite words indexed by $k \in \Ni \cup \{+\infty\}$ where $\Ni$ denotes the set of positive integers. Two finite words $u$ and $v$ in…
Much like sentences are composed of words, words themselves are composed of smaller units. For example, the English word questionably can be analyzed as question+able+ly. However, this structural decomposition of the word does not directly…
In this work we explore the dissimilarity between symmetric word pairs, by comparing the inter-word distance distribution of a word to that of its reversed complement. We propose a new measure of dissimilarity between such distributions.…
Fraenkel and Simpson showed that the number of distinct squares in a word of length n is bounded from above by 2n, since at most two distinct squares have their rightmost, or last, occurrence begin at each position. Improvements by Ilie to…
A language is dense if the set of all infixes (or subwords) of the language is the set of all words. Here, it is shown that it is decidable whether the language accepted by a nondeterministic Turing machine with a one-way read-only input…
In this paper, we analyze the density of the Fibonacci word and its derived forms by examining the morphisms associated with each. It offers a comparative analysis of the density of Fibonacci numbers alongside other words derived from…
Any finite word $w$ of length $n$ contains at most $n+1$ distinct palindromic factors. If the bound $n+1$ is reached, the word $w$ is called rich. The number of rich words of length $n$ over an alphabet of cardinality $q$ is denoted…
We consider the problem of finding a homomorphism from an input digraph $G$ to a fixed digraph $H$. We show that if $H$ admits a weak-near-unanimity polymorphism $\phi$ then deciding whether $G$ admits a homomorphism to $H$ (HOM($H$)) is…
Word matches are often used in sequence comparison methods, either as a measure of sequence similarity or in the first search steps of algorithms such as BLAST or BLAT. The D2 statistic is the number of matches of words of k letters between…
A binary word is symmetric if it is a palindrome or an antipalindrome. We define a new measure of asymmetry of a binary word equal to the minimal number of letters of the word whose deleting from the word yields a symmetric word and obtain…
A pair of letters $x$ and $y$ are said to alternate in a word $w$ if, after removing all letters except for the copies of $x$ and $y$ from $w$, the resulting word is of the form $xyxy\ldots$ (of even or odd length) or $yxyx\ldots$ (of even…
A binary word is Sturmian if the occurrences of each letter are balanced, in the sense that in any two factors of the same length, the difference between the number of occurrences of the same letter is at most 1. In digital geometry,…
We show that the equality language of two non-periodic binary morphisms is generated by at most two words. If its rank is two, then the generators start (and end) with different letters. This in particular implies that any binary language…
We prove that, for any pure morphic word $w$, if the frequencies of all letters in $w$ exist, then the frequencies of all factors in $w$ exist as well. This result answers a question of Saari in his doctoral thesis.
We examine the evolution of a universe comprising two interacting fluids, which interact via a term proportional to the product of their densities. In the case of two matter fluids it is shown that the ratio of the densities tends to a…