  Let $\mathfrak{C}$ be a class of finite combinatorial structures. The
\textit{profile} of $\mathfrak{C}$ is the function $\varphi_{\mathfrak{C}}$
which counts, for every integer $n$, the number $\varphi_{\mathfrak{C}}(n)$ of
members of $\mathfrak{C}$ defined on $n$ elements, isomorphic structures been
identified. The \textit{generating function of} $\mathfrak{C}$ is $\mathcal
{H}_{\mathfrak{C}}(x):=\sum_{n\geqq 0}\varphi_{\mathfrak{C}}(n)x^{n}$. Many
results about the behavior of the function $\varphi_{\mathfrak{C}}$ have been
obtained. Albert and Atkinson have shown that the generating series of several
classes of permutations are algebraic. In this paper, we show how their results
extend to classes of ordered binary relational structures; putting emphasis on
the notion of hereditary well quasi order, we discuss some of their questions
and answer one.

Combinatorics