As already mentioned in Introduction, an infinite binary word u is a complementary-symmetric Rote word if its factor complexity satisfies [C.

A narrow connection between infinite binary words rich in classical palindromes and infinite binary words rich simultaneously in palindromes and pseudopalindromes (the so-called H-rich words) is demonstrated.

If f is a binary word and d a positive integer, then the generalized Fibonacci cube [Q.

If f is an arbitrary binary word and d is a positive integer, then the generalized Fibonacci cube [Q.

The assembly measures the absolute phase difference between IF inputs and produces a representative eight-bit

binary word at its output.

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]].

A quadruple ([alpha], [beta]; [gamma], [delta]) is said to be the boundary of a rhomboid-shaped Knutson-Tao-puzzle P if [alpha] equals the binary word that is obtained by reading the labels along the leftmost NE-SW diagonal of P from left to right, [beta] equals the word that is obtained by reading the labels along the rightmost NW-SE diagonal of P from left to right, [gamma] equals the word that is obtained by reading the labels along the rightmost NE-SW diagonal of P from left to right and [delta] the binary word that is obtained by reading the labels along the leftmost NW-SE diagonal of P from left to right.

Any infinite cubefree

binary word must contain squares; however, Dekking [9] 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]).

Recall that the descents of an ordinary composition are the positions of the ones in the associated

binary word.

More precisely, for a finite or infinite

binary word x = [x.

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.

nn], then, count zigzag-free

binary words with are equal number of zeros and ones.