PROFILE AND HEREDITARY CLASSES OF ORDERED RELATIONAL STRUCTURES

ABSTRACT. Let C be a class of finite combinatorial structures. The profile of C is the function ϕC which counts, for every integer n, the number ϕC(n) of members of C defined on n elements, isomorphic structures been identified. The generating function of C is HC(x):= n=0 ϕC(n)x n. Many results about the behavior of the function ϕC 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