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Published in:
2013 | OriginalPaper | Chapter
On the Number of Unbordered Factors
Authors : Daniel Goč, Hamoon Mousavi, Jeffrey Shallit
Published in: Language and Automata Theory and Applications
Publisher: Springer Berlin Heidelberg
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We illustrate a general technique for enumerating factors of
k
-automatic sequences by proving a conjecture on the number
f
(
n
) of unbordered factors of the Thue-Morse sequence. We show that
f
(
n
) ≤
n
for
n
≥ 4 and that
f
(
n
) =
n
infinitely often. We also give examples of automatic sequences having exactly 2 unbordered factors of every length.