相关论文: Quasi-random words and limits of word sequences
We consider the number of occurrences of subwords (non-consecutive sub-sequences) in a given word. We first define the notion of subword entropy of a given word that measures the maximal number of occurrences among all possible subwords. We…
We define and study a natural category of graph limits. The objects are pairs $(\pi,\mu)$, where $\pi$ (the distribution of vertices) is an abstract probability measure on some abstract measurable space $(X,\mathcal{A})$ and $\mu$ (the…
In this paper, we introduce a convergence notion for ordered selections. Our convergence notion is based on subpermutation densities and convergences of the marginal distributions. A particular case of this convergence is the well-known…
In this paper we consider the normalized lengths of the factors of some factorizations of random words. First, for the \emph{Lyndon factorization} of finite random words with $n$ independent letters drawn from a finite or infinite totally…
The goal of the paper is to lay the foundation for the qualitative analogue of the classical, quantitative sparse graph limit theory. In the first part of the paper we introduce the qualitative analogues of the Benjamini-Schramm and…
We deal with countable alphabet locally compact random subshifts of finite type (the latter merely meaning that the symbol space is generated by an incidence matrix) under the absence of Big Images Property and under the absence of uniform…
An important body of quantitative linguistics is constituted by a series of statistical laws about language usage. Despite the importance of these linguistic laws, some of them are poorly formulated, and, more importantly, there is no…
We checked that the distribution of words in text should uniform, which gives Heaps' law as natural result, that is, the number of types of words can be expressed as a power law of the number of tokens within text. We developed a…
The subword complexity of a word $w$ over a finite alphabet $\mathcal{A}$ is a function that assigns for each positive integer $n$, the number of distinct subwords of length $n$ in $w$. The subword complexity of a word is a good measure of…
We develop a theory of limits for sequences of dense abstract simplicial complexes, where a sequence is considered convergent if its homomorphism densities converge. The limiting objects are represented by stacks of measurable [0,1]-valued…
Quasi-Sturmian words, which are infinite words with factor complexity eventually $n+c$ share many properties with Sturmian words. In this paper, we study the quasi-Sturmian colorings on regular trees. There are two different types, bounded…
One of the main questions that arise when studying random and quasi-random structures is which properties P are such that any object that satisfies P "behaves" like a truly random one. In the context of graphs, Chung, Graham, and Wilson…
Motivated by a recent random pipe dream model, we study a family of probability distributions on \(S_n\) arising from Bott--Samelson varieties over finite fields. More precisely, for a word \(R\), we consider the Bott--Samelson map…
Superpermutations are words over a finite alphabet containing every permutation as a factor. Finding the minimal length of a superpermutation is still an open problem. In this article, we introduce superpermutations matrices. We establish a…
We study the asymptotics and fine-scale behavior of quantitative combinatorial measures of infinite words and related dynamical and algebraic structures. We construct infinite recurrent words $w$ whose complexity functions $p_w(n)$ are…
We establish some limit theorems for quasi-arithmetic means of random variables. This class of means contains the arithmetic, geometric and harmonic means. Our feature is that the generators of quasi-arithmetic means are allowed to be…
We consider sequences of graphs and define various notions of convergence related to these sequences: ``left convergence'' defined in terms of the densities of homomorphisms from small graphs into the graphs of the sequence, and ``right…
Suppose a $k$-uniform hypergraph $H$ that satisfies a certain regularity instance (that is, there is a partition of $H$ given by the hypergraph regularity lemma into a bounded number of quasirandom subhypergraphs of prescribed densities).…
The literature on word-representable graphs is quite rich, and a number of variations of the original definition have been proposed over the years. We are initiating a systematic study of such variations based on formal languages. In our…
Driven by the interest of reasoning about probabilistic programming languages, we set out to study a notion of unicity of normal forms for them. To provide a tractable proof method for it, we define a property of distribution confluence…