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

E-mail:mcintosh@servidor.unam.mx