Related papers: Relations on words
We survey known results and open problems in abelian combinatorics on words. Abelian combinatorics on words is the extension to the commutative setting of the classical theory of combinatorics on words. The extension is based on…
In combinatorics on words, a classical topic of study is the number of specific patterns appearing in infinite sequences. For instance, many works have been dedicated to studying the so-called factor complexity of infinite sequences, which…
Certain upper triangular matrices, termed as Parikh matrices, are often used in the combinatorial study of words. Given a word, the Parikh matrix of that word elegantly computes the number of occurrences of certain predefined subwords in…
This paper is an extended abstract of the dissertation presented by the author for the doctoral degree in physics and mathematics (in Russia). The main characteristic studied in the dissertation is combinatorial complexity, which is a…
The paper is a survey of notions and results related to classical and new generalizations of the notion of a periodic sequence. The topics related to almost periodicity in combinatorics on words, symbolic dynamics, expressibility in logical…
In this paper we study the maximal pattern complexity of infinite words up to Abelian equivalence. We compute a lower bound for the Abelian maximal pattern complexity of infinite words which are both recurrent and aperiodic by projection.…
The paper explores combinatorial properties of Fibonacci words and their generalizations within the framework of combinatorics on words. These infinite sequences, measures the diversity of subwords in Fibonacci words, showing non-decreasing…
We say that two finite words $u$ and $v$ are abelian equivalent if and only if they have the same number of occurrences of each letter, or equivalently if they define the same Parikh vector. In this paper we investigate various abelian…
We construct new examples of non-nil algebras with any number of generators, which are direct sums of two locally nilpotent subalgebras. As all previously known examples, our examples are contracted semigroup algebras and the underlying…
Identifying the relations that exist between words (or entities) is important for various natural language processing tasks such as, relational search, noun-modifier classification and analogy detection. A popular approach to represent the…
Two words are $k$-binomially equivalent if each subword of length at most $k$ occurs the same number of times in both words. The $k$-binomial complexity of an infinite word is a counting function that maps $n$ to the number of $k$-binomial…
We employ the notions of `sequential function' and `interrogation' (dialogue) in order to define new partial combinatory algebra structures on sets of functions. These structures are analyzed using J. Longley's preorder-enriched category of…
Classically in combinatorics on words one studies unavoidable regularities that appear in sufficiently long strings of symbols over a fixed size alphabet. In this paper we take another viewpoint and focus on combinatorial properties of long…
There have been several efforts to extend distributional semantics beyond individual words, to measure the similarity of word pairs, phrases, and sentences (briefly, tuples; ordered sets of words, contiguous or noncontiguous). One way to…
Abelian complexity of a word $\mathbf{u}$ is a function that counts the number of pairwise non-abelian-equivalent factors of $\mathbf{u}$ of length $n$. We prove that for any $c$-balanced Parry word $\mathbf{u}$, the values of the abelian…
We use results on Dyck words and lattice paths to derive a formula for the exact number of binary words of a given length with a given minimal abelian border length, tightening a bound on that number from Christodoulakis et al. (Discrete…
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…
In this paper we introduce and study a family of complexity functions of infinite words indexed by $k \in \ints ^+ \cup {+\infty}.$ Let $k \in \ints ^+ \cup {+\infty}$ and $A$ be a finite non-empty set. Two finite words $u$ and $v$ in $A^*$…
We introduce the $k$-bonacci polyominoes, a new family of polyominoes associated with the binary words avoiding $k$ consecutive $1$'s, also called generalized $k$-bonacci words. The polyominoes are very entrancing objects, considered in…
As suggested by Currie, we apply the probabilistic method to problems regarding pattern avoidance. Using techniques from analytic combinatorics, we calculate asymptotic pattern occurrence statistics and use them in conjunction with the…