1 research outputs found
A new complexity function, repetitions in Sturmian words, and irrationality exponents of Sturmian numbers
We introduce and study a new complexity function in combinatorics on words,
which takes into account the smallest second occurrence time of a factor of an
infinite word. We characterize the eventually periodic words and the Sturmian
words by means of this function. Then, we establish a new result on repetitions
in Sturmian words and show that it is best possible. Let be an
integer. We deduce a lower bound for the irrationality exponent of real numbers
whose sequence of -ary digits is a Sturmian sequence over and we prove that this lower bound is best possible. As an application,
we derive some information on the -ary expansion of
,for any integer .Comment: 38 page