Related papers: The sigma-sequence and counting occurrences of som…
The introduction of Parikh matrices by Mateescu et al. in 2001 has sparked numerous new investigations in the theory of formal languages by various researchers, among whom is Serbanuta. Recently, a decade-old conjecture by Serbanuta on the…
A palindromic periodicity is a factor of an infinite word $(ps)^\omega$ where $p$ and $s$ are palindromes and the factor has length at least $|ps|$, for example, $accabaccab$. In this paper we describe several ways in which a palindromic…
Segmental structure is a common pattern in many types of sequences such as phrases in human languages. In this paper, we present a probabilistic model for sequences via their segmentations. The probability of a segmented sequence is…
Dictionaries are inherently circular in nature. A given word is linked to a set of alternative words (the definition) which in turn point to further descendants. Iterating through definitions in this way, one typically finds that…
We introduce and study a generalized Parikh matrix mapping based on tracking the occurrence counts of special types of subsequences. These matrices retain more information about a word than the original Parikh matrix mapping while…
Recent observations in the theory of verse and empirical metrics have suggested that constructing a verse line involves a pattern-matching search through a source text, and that the number of found elements (complete words totaling a…
In the following pages we discuss infinite sequences defined on a finite alphabet, and more specially those which are generated by finite automata. We have divided our paper into seven parts which are more or less self-contained. Needless…
We present a model of speech perception which takes into account effects of correlations between sounds. Words in this model correspond to the attractors of a suitably chosen descent dynamics. The resulting lexicon is rich in short words,…
This paper gives a short overview of Zimin words, and proves an interesting property of their distribution. Let $L_q^m$ to be the lexically ordered sequence of $q$-ary words of length $m$, and let $T_n(L_q^m)$ to be the binary sequence…
We consider a component of the word statistics known as clump; starting from a finite set of words, clumps are maximal overlapping sets of these occurrences. This parameter has first been studied by Schbath with the aim of counting the…
We introduce a class of stochastic integer sequences. In these sequences, every element is a sum of two previous elements, at least one of which is chosen randomly. The interplay between randomness and memory underlying these sequences…
A problem of reconstructing words from their subwords involves determining the minimum amount of information needed, such as multisets of scattered subwords of a specific length or the frequency of scattered subwords from a given set, in…
This paper is about counting the number of distinct (scattered) subwords occurring in a given word. More precisely, we consider the generalization of the Pascal triangle to binomial coefficients of words and the sequence $(S(n))_{n\ge 0}$…
This article presents a pattern-based language designed to select (a set of) subterms of a given term in a concise and robust way. Building on this language, we implement a single-step rewriting tactic in the Isabelle theorem prover, which…
We consider a random permutation drawn from the set of 132-avoiding permutations of length $n$ and show that the number of occurrences of another pattern $\sigma$ has a limit distribution, after scaling by $n^{\lambda(\sigma)/2}$ where…
We study compositions whose parts are colored by subsequences of the Fibonacci numbers. We give explicit bijections between Fibonacci colored compositions and several combinatorial objects, including certain restricted ternary and…
The aim of this note is to survey the factorizations of the Fibonacci infinite word that make use of the Fibonacci words and other related words, and to show that all these factorizations can be easily derived in sequence starting from…
We consider the infinite one-sided sequence over alphabet $\{a,b\}$ generated by the period-doubling substitution $\sigma(a)=ab$ and $\sigma(b)=aa$, denoted by $\mathbb{D}$. Let $r_p(\omega)$ be the $p$-th return word of factor $\omega$.…
The equidistant subsequence pattern matching problem is considered. Given a pattern string $P$ and a text string $T$, we say that $P$ is an \emph{equidistant subsequence} of $T$ if $P$ is a subsequence of the text such that consecutive…
We propose a novel approach to learn word embeddings based on an extended version of the distributional hypothesis. Our model derives word embedding vectors using the etymological composition of words, rather than the context in which they…