  Central, standard, and Christoffel words are three strongly interrelated
classes of binary finite words which represent a finite counterpart of
characteristic Sturmian words. A natural arithmetization of the theory is
obtained by representing central and Christoffel words by irreducible fractions
labeling respectively two binary trees, the Raney (or Calkin-Wilf) tree and the
Stern-Brocot tree. The sequence of denominators of the fractions in Raney's
tree is the famous Stern diatomic numerical sequence. An interpretation of the
terms $s(n)$ of Stern's sequence as lengths of Christoffel words when $n$ is
odd, and as minimal periods of central words when $n$ is even, allows one to
interpret several results on Christoffel and central words in terms of Stern's
sequence and, conversely, to obtain a new insight in the combinatorics of
Christoffel and central words by using properties of Stern's sequence. One of
our main results is a non-commutative version of the "alternating bit sets
theorem" by Calkin and Wilf. We also study the length distribution of
Christoffel words corresponding to nodes of equal height in the tree, obtaining
some interesting bounds and inequalities.
