We study aperiodic balanced sequences over finite alphabets. A sequence v of this type is
fully characterised by a Sturmian sequence u and two constant gap sequences y and y …

The repetition threshold of a class C of infinite d-ary sequences is the smallest real number r
such that in the class C there exists a sequence that avoids e-powers for all e> r. This notion …

The complement $\overline {x} $ of a binary word $ x $ is obtained by changing each $0 $ in
$ x $ to $1 $ and vice versa. We study infinite binary words $\bf w $ that avoid sufficiently …

The critical exponent $ E (\mathbf u) $ of an infinite sequence $\mathbf u $ over a finite
alphabet expresses the maximal repetition of a factor in $\mathbf u $. By the famous …

We say a binary word is good if the only antisquares it contains are 01 and 10. We
characterize the minimal antisquares, that is, those words that are antisquares but all proper …

In 2014, Vesti proposed the problem of determining the repetition threshold for infinite rich
words, ie, for infinite words in which all factors of length $ n $ contain $ n $ distinct nonempty …

We colour the Fibonacci sequence by suitable constant gap sequences to provide an upper
bound on the asymptotic repetition threshold of d-ary balanced sequences. The bound is …

The asymptotic critical exponent measures for a sequence the maximum repetition rate of
factors of growing length. The infimum of asymptotic critical exponents of sequences of a …

This work aims to discover and develop links between three related but distinct
mathematical domains: combinatorics on words, number theory and discrete geometry …

Tato práce rozvíjí souvislosti mezi kombinatorikou na slovech, teorií čísel a diskrétní
geometrií. V rámci kombinatoriky na slovech jsou zkoumána Arnouxova–Rauzova slova a …