Squares (fragments of the form xx, for some string x) are arguably the most natural type of
repetition in strings. The basic algorithmic question concerning squares is to check if a given …

String matching is one of the oldest algorithmic techniques, yet still one of the most
pervasive in computer science. The past 20 years have seen technological leaps in …

A {\em square} is a word of the form $ uu $. In this paper we prove that for a given finite word
$ w $, the number of distinct square factors of $ w $ is bounded by $| w|-|\Alphabet (w)|+ 1 …

Internationally recognised researchers look at developing trends in combinatorics with
applications in the study of words and in symbolic dynamics. They explain the important …

A square is a word of the form uu, where u is a finite word. The problem of determining the
number of distinct squares in a finite word was initially explored by Fraenkel and Simpson in …

Given a string on an integer alphabet, we present an algorithm that computes the set of all
distinct squares belonging to this string in time linear to the string length. As an application …

The notions of periodicity and repetitions in strings, and hence these of runs and squares,
naturally extend to two-dimensional strings. We consider two types of repetitions in 2D …

A string T of length m is periodic in P of length p if P is a substring of T and T [i]= T [i+ p] for all
0≤ i≤ m− p− 1 and m≥ 2 p. The shortest such prefix, P, is called the period of T (ie, P= T …

We consider the problem of preprocessing a text $ T $ of length $ n $ and a dictionary
$\mathcal {D} $ in order to be able to efficiently answer queries $ CountDistinct (i, j) $, that is …

A 2D string is simply a 2D array. We continue the study of the combinatorial properties of
repetitions in such strings over the binary alphabet, namely the number of distinct tandems …