相关论文: Words restricted by patterns with at most 2 distin…
We characterize the formulas that are avoided by every $\alpha$-free word for some $\alpha>1$. We study the avoidability index of formulas whose fragments are of the form $XYX$. The largest avoidability index of an avoidable palindrome…
In this note we present a characterisation of all unary and binary patterns that do not only contain variables, but also reversals of their instances. These types of variables were studied recently in either more general or particular…
In the present paper we consider biologically motivated reduction operations on double occurrence words. Then we define the nesting index of a double occurrence word to be the least number of reduction operations it takes for a word to be…
This paper is continuation of the study of the 1-box pattern in permutations introduced by the authors in \cite{kitrem4}. We derive a two-variable generating function for the distribution of this pattern on 132-avoiding permutations, and…
Learning word embeddings using distributional information is a task that has been studied by many researchers, and a lot of studies are reported in the literature. On the contrary, less studies were done for the case of multiple languages.…
A reconstruction problem of words from scattered factors asks for the minimal information, like multisets of scattered factors of a given length or the number of occurrences of scattered factors from a given set, necessary to uniquely…
We study subshift that arise by excluding words of length two from Dyck shifts. The words that are to be excluded are taken from a finite set that is not literal-uniform.
We introduce Peano words, which are words corresponding to finite approximations of the Peano space filling curve. We then find the number of occurrences of certain patterns in these words.
The complement $\overline{x}$ of a binary word $x$ is obtained by changing each $0$ in $x$ to $1$ and vice versa. We study infinite binary words $\bf w$ that avoid sufficiently large complementary factors; that is, if $x$ is a factor of…
The dependence of the frequency distributions due to multiple meanings of words in a text is investigated by deleting letters. By coding the words with fewer letters the number of meanings per coded word increases. This increase is measured…
Word segmentation, the problem of finding word boundaries in speech, is of interest for a range of tasks. Previous papers have suggested that for sequence-to-sequence models trained on tasks such as speech translation or speech recognition,…
In 2011, Fici and Lipt\'ak introduced prefix normal words. A binary word is prefix normal if it has no factor (substring) that contains more occurrences of the letter 1 than the prefix of the same length. Among the open problems regarding…
Recently, Babson and Steingrimsson have introduced generalised permutation patterns that allow the requirement that two adjacent letters in a pattern must be adjacent in the permutation. We consider pattern avoidance for such patterns, and…
Motivated by the recent proof of the Stanley-Wilf conjecture, we study the asymptotic behavior of the number of permutations avoiding a generalized pattern. Generalized patterns allow the requirement that some pairs of letters must be…
The difficulties of automatic extraction of definitions and methods from scientific documents lie in two aspects: (1) the complexity and diversity of natural language texts, which requests an analysis method to support the discovery of…
Combinatorial properties of maximal repetitions (runs) in formal words are studied. We classify all maximal repetitions in a word as primary and secondary where the set of all primary repetitions determines all the other repetitons in the…
Rich words are characterized by containing the maximum possible number of distinct palindromes. Several characteristic properties of rich words have been studied; yet the analysis of repetitions in rich words still involves some interesting…
We present a method, illustrated by several examples, to find explicit counts of permutations containing a given multiset of three letter patterns. The method is recursive, depending on bijections to reduce to the case of a smaller…
The word inference problem is to determine languages such that the information on the number of occurrences of those subwords in the language can uniquely identify a word. A considerable amount of work has been done on this problem, but the…
A closed word (a.k.a. periodic-like word or complete first return) is a word whose longest border does not have internal occurrences, or, equivalently, whose longest repeated prefix is not right special. We investigate the structure of…