327 research outputs found
Transduction of Automatic Sequences and Applications
We consider the implementation of the transduction of automatic sequences,
and their generalizations, in the Walnut software for solving decision problems
in combinatorics on words. We provide a number of applications, including (a)
representations of n! as a sum of three squares (b) overlap-free Dyck words and
(c) sums of Fibonacci representations. We also prove results about iterated
running sums of the Thue-Morse sequence
Latin Square Thue-Morse Sequences are Overlap-Free
We define a morphism based upon a Latin square that generalizes the
Thue-Morse morphism. We prove that fixed points of this morphism are
overlap-free sequences generalizing results of Allouche - Shallit and Frid.Comment: 5 pages, 1 figur
On the critical exponent of generalized Thue-Morse words
For certain generalized Thue-Morse words t, we compute the "critical
exponent", i.e., the supremum of the set of rational numbers that are exponents
of powers in t, and determine exactly the occurrences of powers realizing it.Comment: 13 pages; to appear in Discrete Mathematics and Theoretical Computer
Science (accepted October 15, 2007
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 patterns in the Prouhet-Thue-Morse sequence
We show that, with the exception of the words and , all
(finite or infinite) binary patterns in the Prouhet-Thue-Morse sequence can
actually be found in that sequence as segments (up to exchange of letters in
the infinite case). This result was previously attributed to unpublished work
by D. Guaiana and may also be derived from publications of A. Shur only
available in Russian. We also identify the (finitely many) finite binary
patterns that appear non trivially, in the sense that they are obtained by
applying an endomorphism that does not map the set of all segments of the
sequence into itself
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