Related papers: Application of entropy compression in pattern avoi…
We examine words w satisfying the following property: if x is a subword of w and |x| is at least k for some fixed k, then the reversal of x is not a subword of w.
A word $w$ over an alphabet $\Sigma$ is a Lyndon word if there exists an order defined on $\Sigma$ for which $w$ is lexicographically smaller than all of its conjugates (other than itself). We introduce and study \emph{universal Lyndon…
Let $w$ be a finite word of length $n$. In this paper, we study the maximum possible number of distinct rational power factors in a finite word. A rational power is a word of the form $u=p^kp'$, where $p$ is a nonempty finite word, $k$ is…
We consider the problem of constructing prefix-free codes in which a designated symbol, a space, can only appear at the end of codewords. We provide a linear-time algorithm to construct almost-optimal codes with this property, meaning that…
Vincular and covincular patterns are generalizations of classical patterns allowing restrictions on the indices and values of the occurrences in a permutation. In this paper we study the integer sequences arising as the enumerations of…
Two words $w_1$ and $w_2$ are said to be $k$-binomial equivalent if every non-empty word $x$ of length at most $k$ over the alphabet of $w_1$ and $w_2$ appears as a scattered factor of $w_1$ exactly as many times as it appears as a…
We study the properties of the uncountable set of Stewart words. These are Toeplitz words specified by infinite sequences of Toeplitz patterns of the form $\alpha\beta\gamma$, where $\alpha,\beta,\gamma$ is any permutation of the symbols…
Various grammar compression algorithms have been proposed in the last decade. A grammar compression is a restricted CFG deriving the string deterministically. An efficient grammar compression develops a smaller CFG by finding duplicated…
We consider pattern containment and avoidance with a very tight definition that was used first by Riordan more than 60 years ago. Using this definition, we prove the monotone pattern is easier to avoid than almost any other pattern of the…
The $k$-mappability problem has two integers parameters $m$ and $k$. For every subword of size $m$ in a text $S$, we wish to report the number of indices in $S$ in which the word occurs with at most $k$ mismatches. The problem was lately…
We discuss the notion of privileged word, recently introduced by Peltomaki. A word w is privileged if it is of length <=1, or has a privileged border that occurs exactly twice in w. We prove the following results: (1) if w^k is privileged…
The elimination distance to some target graph property P is a general graph modification parameter introduced by Bulian and Dawar. We initiate the study of elimination distances to graph properties expressible in first-order logic. We…
The exponent of a word is the ratio of its length over its smallest period. The repetitive threshold r(a) of an a-letter alphabet is the smallest rational number for which there exists an infinite word whose finite factors have exponent at…
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…
The problem of compression in standard information theory consists of assigning codes as short as possible to numbers. Here we consider the problem of optimal coding -- under an arbitrary coding scheme -- and show that it predicts Zipf's…
The traditional methods for data compression are typically based on the symbol-level statistics, with the information source modeled as a long sequence of i.i.d. random variables or a stochastic process, thus establishing the fundamental…
A factor $u$ of a word $w$ is a cover of $w$ if every position in $w$ lies within some occurrence of $u$ in $w$. A word $w$ covered by $u$ thus generalizes the idea of a repetition, that is, a word composed of exact concatenations of $u$.…
A graph $G=(V,E)$ is representable if there exists a word $W$ over the alphabet $V$ such that letters $x$ and $y$ alternate in $W$ if and only if $(x,y)\in E$ for each $x\neq y$. If $W$ is $k$-uniform (each letter of $W$ occurs exactly $k$…
Let $P = \{p(i)\}$ be a measure of strictly positive probabilities on the set of nonnegative integers. Although the countable number of inputs prevents usage of the Huffman algorithm, there are nontrivial $P$ for which known methods find a…
Catalan words are particular growth-restricted words over the set of non-negative integers, and they represent still another combinatorial class counted by the Catalan numbers. We study the distribution of descents on the sets of Catalan…