相关论文: Complexes of Injective Words and Their Commutation…
A word is called closed if it has a prefix which is also its suffix and there is no internal occurrences of this prefix in the word. In this paper we study words that are rich in closed factors, i.e., which contain the maximal possible…
In a \emph{weighted sequence}, for every position of the sequence and every letter of the alphabet a probability of occurrence of this letter at this position is specified. Weighted sequences are commonly used to represent imprecise or…
The occurrence of unknown words in texts significantly hinders reading comprehension. To improve accessibility for specific target populations, computational modelling has been applied to identify complex words in texts and substitute them…
Let $f_W(n)$ be the number of different factors of length $n$ appearing in $W$. A classical result of Morse and Hedlund, stated in 1938, asserts that an infinite word $W$ is ultimately periodic if and only if $f_W(n)\leq n$ for some $n\in…
Different semantic interpretation tasks such as text entailment and question answering require the classification of semantic relations between terms or entities within text. However, in most cases it is not possible to assign a direct…
A word $w$ is said to be closed if it has a proper factor $x$ which occurs exactly twice in $w$, as a prefix and as a suffix of $w$. Based on the concept of Ziv-Lempel factorization, we define the closed $z$-factorization of finite and…
We characterize the infinite words determined by indexed languages. An infinite language $L$ determines an infinite word $\alpha$ if every string in $L$ is a prefix of $\alpha$. If $L$ is regular or context-free, it is known that $\alpha$…
We discuss a topological approach to words introduced by the author. Words on an arbitrary alphabet are approximated by Gauss words and then studied up to natural modifications inspired by the Reidemeister moves on knot diagrams. This leads…
The article studies power complexes and generalized power complexes, and investigates the algebraic structure of their automorphism groups. The combinatorial incidence structures involved are cube-like, in the sense that they have many…
We develop the theory of mixed finite elements in terms of special inverse systems of complexes of differential forms, defined over cellular complexes. Inclusion of cells corresponds to pullback of forms. The theory covers for instance…
A finite word $w$ of length $n$ contains at most $n+1$ distinct palindromic factors. If the bound $n+1$ is attained, the word $w$ is called rich. An infinite word $w$ is called rich if every finite factor of $w$ is rich. Let $w$ be a word…
This paper studies combinatorial properties of the 'complex of planar injective words', a chain complex of modules over the Temperley-Lieb algebra that arose in our work on homological stability. Despite being a linear rather than a…
We investigate the state complexity of the permutation operation, or the commutative closure, on Alphabetical Pattern Constraints (APC). This class corresponds to level $3/2$ of the Straubing-Th{\'e}rien Hierarchy and includes the finite,…
In this paper, we consider infinite words that arise as fixed points of primitive substitutions on a finite alphabet and finite colorings of their factors. Any such infinite word exhibits a "hierarchal structure" that will allow us to…
Gottschalk's surjunctivity conjecture states that for all group universes and finite alphabets, every equivariant and continuous selfmap of the full shift, known as cellular automaton, cannot be a strict embedding. Not all surjective…
We study the $k$-Bonacci word over the infinite alphabet $\mathbb{N}$. Since the alphabet is infinite, the usual factor complexity is infinite and does not provide any information. We therefore investigate factor occurrence statistics in…
We present an impossibility result, called a theorem about facts and words, which pertains to a general communication system. The theorem states that the number of distinct words used in a finite text is roughly greater than the number of…
Suppose that Alice and Bob are given each an infinite string, and they want to decide whether their two strings are in a given relation. How much communication do they need? How can communication be even defined and measured for infinite…
A special inverse monoid is one defined by a presentation where all the defining relations have the form $r = 1$. By a result of Ivanov Margolis and Meakin the word problem for such an inverse monoid can often be reduced to the word problem…
Consider a graph with vertex set S. A word in the alphabet S has the intervening neighbours property if any two occurrences of the same letter are separated by all its graph neighbours. For a Coxeter graph, words represent group elements.…