As already mentioned in Introduction, an infinite binary word
u is a complementary-symmetric Rote word if its factor complexity satisfies [C.sub.u](n) = 2n for all n [greater than or equal to] 1 and its language is closed under the exchange of the two letters E.
If f is a binary word
and d a positive integer, then the generalized Fibonacci cube [Q.sub.d](f) is the graph obtained from the d-cube [Q.sub.d] by removing all the vertices that contain f as a factor, while the generalized Lucas cube [Q.sub.d]([??]) is the graph obtained from [Q.sub.d] by removing all the vertices that have a circulation containing f as a factor.
Since there are N = B measurements, the bth measurement provides the bth digit of the B-digit binary word
, for 1 [less than or equal to] b [less than or equal to] B.
where each [[beta].sub.i] is a distinct length-n binary word
. Then, the following layout for [Q.sub.2](n+1)
The assembly measures the absolute phase difference between IF inputs and produces a representative eight-bit binary word
at its output.
King (1980) first proposed that the pattern of entries in each row or column of the part/machine matrix be read as a binary word
, and that rows or columns be rearanged in order of decreasing binary word
[d.sub.m], its support is defined as the binary word
Given a binary word
[omega] of length N the number of zeroes in [omega] between the (j - 1)-st and the j-th one in [omega], where the ones are counted from left to right, is denoted by [[absolute value of [omega]].sub.0,j] for 2 [less than or equal to] j [less than or equal to] [[absolute value of [omega]].sub.1].
Any infinite cubefree binary word
must contain squares; however, Dekking  proved that there exists an infinite cubefree binary word
containing no squares xx where the length of x is greater than 3 (see also [14, 15]).
Now, define for any composition I = ([i.sub.0], ..., [i.sub.r]), the binary word
: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
In the above setting, the problem is of finding, for any infinite binary word
x, relations between the quantities
In order to fix the problem, in [T.sub.l], we replace the sequence [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] with a new sequence [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] of infinite binary words
, close to the [t.sub.[upsilon]]'s but independent, defined as follows: let [([[zeta].sub.i]).sub.j[member of]N] be an i.i.d.