Let us suppose a and b are letters, and that x is a sequence,
possibly null and possibly empty. We define the merged product of the
sequences s and t, denoted 
by
Likewise, define the overlap, 
by
These are just the combinations of indices required to work with the
de Bruijn matrices. For example, the 
column-stochastic
matrix is defined in terms of n- and 
-block probabilities by
the formula
Correspondingly the row-stochastic matrix is defined by
Unless stated otherwise, we will assume that a probabilistic de Bruijn matrix is column-stochastic. Since it is not always convenient to show the matrix elements as a quotient, but it is essential to know which of them intrinsically vanish, let us write
and note that it vanishes unless x=y, or alternatively when 