6,875 research outputs found
Binary words containing infinitely many overlaps
We characterize the squares occurring in infinite overlap-free binary words
and construct various alpha power-free binary words containing infinitely many
overlaps.Comment: 9 page
Binary Words Containing Infinitely Many Overlaps
We characterize the squares occurring in infinite overlap-free binary words and construct various α power-free binary words containing infinitely many overlaps.http://www.combinatorics.org/Volume_13/Abstracts/v13i1r82.htm
Languages invariant under more symmetries: overlapping factors versus palindromic richness
Factor complexity and palindromic complexity of
infinite words with language closed under reversal are known to be related by
the inequality for any \,. Word for which
the equality is attained for any is usually called rich in palindromes. In
this article we study words whose languages are invariant under a finite group
of symmetries. For such words we prove a stronger version of the above
inequality. We introduce notion of -palindromic richness and give several
examples of -rich words, including the Thue-Morse sequence as well.Comment: 22 pages, 1 figur
Anti-Powers in Infinite Words
In combinatorics of words, a concatenation of consecutive equal blocks is
called a power of order . In this paper we take a different point of view
and define an anti-power of order as a concatenation of consecutive
pairwise distinct blocks of the same length. As a main result, we show that
every infinite word contains powers of any order or anti-powers of any order.
That is, the existence of powers or anti-powers is an unavoidable regularity.
Indeed, we prove a stronger result, which relates the density of anti-powers to
the existence of a factor that occurs with arbitrary exponent. As a
consequence, we show that in every aperiodic uniformly recurrent word,
anti-powers of every order begin at every position. We further show that every
infinite word avoiding anti-powers of order is ultimately periodic, while
there exist aperiodic words avoiding anti-powers of order . We also show
that there exist aperiodic recurrent words avoiding anti-powers of order .Comment: Revision submitted to Journal of Combinatorial Theory Series
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