Related papers: Circular words and applications
We characterize exactly the lengths of binary circular words containing no squares other than 00, 11, and 0101. Key words: combinatorics on words, circular words, necklaces, square-free words, non-repetitive sequences
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…
A word is closed if it contains a proper factor that occurs both as a prefix and as a suffix but does not have internal occurrences, otherwise it is open. We deal with the sequence of open and closed prefixes of Sturmian words and prove…
Logically constrained term rewriting is a relatively new formalism where rules are equipped with constraints over some arbitrary theory. Although there are many recent advances with respect to rewriting induction, completion, complexity…
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…
We introduce a generalization of Pascal triangle based on binomial coefficients of finite words. These coefficients count the number of times a word appears as a subsequence of another finite word. Similarly to the Sierpi\'nski gasket that…
We study Fibonacci compositions, which are compositions of natural numbers that only use Fibonacci numbers, in two different contexts. We first prove inequalities comparing the number of Fibonacci compositions to regular compositions where…
This work lists and describes the main recent strategies for building fixed-length, dense and distributed representations for words, based on the distributional hypothesis. These representations are now commonly called word embeddings and,…
We study growth rates of generalised Fibonacci sequences of a particular structure. These sequences are constructed from choosing two real numbers for the first two terms and always having the next term be either the sum or the difference…
The classical Fibonacci sequence is known to exhibit many fascinating properties. In this paper, we explore the Fibonacci sequence and integer sequences generated by second order linear recurrence relations with positive integer…
In this paper, we present a comprehensive system for the treatment of the topic of limits--conceptually, computationally, and formally. The system addresses fundamental linguistic flaws in the standard presentation of limits, which attempts…
We consider $m$-th order linear recurrences that can be thought of as generalizations of the Lucas sequence. We exploit some interplay with matrices that again can be considered generalizations of the Fibonacci matrix. We introduce the…
The contribution of this paper is to provide a semantic model (using soft constraints) of the words used by web-users to describe objects in a language game; a game in which one user describes a selected object of those composing the scene,…
We define reflective numbers and their iterative summations. We provide classification of reflective numbers based on their iterative cyclical limits.
In this paper, we extend the notion of Lyndon word to transfinite words. We prove two main results. We first show that, given a transfinite word, there exists a unique factorization in Lyndon words that are densely non-increasing, a…
We study the polyregular string-to-string functions, which are certain functions of polynomial output size that can be described using automata and logic. We describe a system of combinators that generates exactly these functions. Unlike…
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…
Prefix normal words are binary words in which each prefix has at least the same number of $\so$s as any factor of the same length. Firstly introduced by Fici and Lipt\'ak in 2011, the problem of determining the index of the prefix…
Motivated by a recent work of Tr\"umper we consider the general Collatz word (up-down pattern) and the sequences following this pattern. The recurrences for the first and last sequence entries are given, obtained from repeated application…
We study possibilities for semantic and syntactic rigidity, i.e., the rigidity with respect to automorphism group and with respect to definable closure. Variations of rigidity and their degrees are studied in general case, for special…