1 research outputs found
Morphic words, Beatty sequences and integer images of the Fibonacci language
Morphic words are letter-to-letter images of fixed points of morphisms on
finite alphabets. There are situations where these letter-to-letter maps do not
occur naturally, but have to be replaced by a morphism. We call this a
decoration of . Theoretically, decorations of morphic words are again
morphic words, but in several problems the idea of decorating the fixed point
of a morphism is useful. We present two of such problems. The first considers
the so called sequences, where is a quadratic irrational, is
the Beatty sequence defined by , and is the
sequence . The second example considers homomorphic embeddings of
the Fibonacci language into the integers, which turns out to lead to
generalized Beatty sequences with terms of the form , where and are integers