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Abstract
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By measuring second occurring times of factors of an infinite word
,
Bugeaud and Kim introduced a new quantity
called the exponent of
repetition of
. It was proved
by Bugeaud and Kim that
if
is a Sturmian word. We determine the value
such that there is
no Sturmian word
satisfying
and
is an accumulation
point of the set of
when
runs over the Sturmian words.
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To the memory of Professor Ichiro
Satake (1927–2014)
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Keywords
combinatorics on words, Sturmian word, continued fraction,
irrationality exponent, irrationality measure
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Mathematical Subject Classification
Primary: 68R15
Secondary: 11A55, 11A63
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Milestones
Received: 9 January 2021
Revised: 18 May 2021
Accepted: 7 June 2021
Published: 13 September 2021
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