Maximal repetitions or runs in strings have a wide array of applications and thus have been
extensively studied. In this paper, we extend this notion to 2-dimensions, precisely defining a …

Combinatorial properties of 1D Fibonacci words is a well studied topic in Formal language
theory. In the year 2000, Apostolico et. al. extended the concept of one dimensional …

We introduce the natural notion of a matching frame in a $2 $-dimensional string. A
matching frame in a $2 $-dimensional $ n\times m $ string $ M $, is a rectangle such that the …

Multidimensional data are widely used in real-life applications. Intel's new brand of SSDs,
called 3D XPoint, is an example of three-dimensional data. Motivated by a structural …

The classical pattern matching asks for locating all occurrences of one string, called the
pattern, in another, called the text, where a string is simply a sequence of characters. Due to …

On the least number of palindromes in two-dimensional words - ScienceDirect Skip to main
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If x is a non-empty string then the repetition xx is called a tandem repeat. Similarly, a tandem
in a two-dimensional array X is a configuration consisting of copies of a same primitive block …

The row-column combination RCC maps two (word) languages over the same alphabet onto
the set of rectangular arrays, ie, pictures, such that each row/column is a word of the …

The tiling systems define the family of recognizable picture languages as the projection of
local picture languages, ie, strictly-locally-testable (SLT) languages of order 2. A basic …

Toroidal codes of pictures are introduced as the generalization of circular codes of strings in
two dimensions. They are characterized by a property of very pureness on a generated …