Let A={a1,…,an,a1−1,…,an−1} and iteration of A denoted by A[starf ] to be the set of words in A (including the empty word). Let S⊆A[starf ]; then the growth function of the set S is the function Γ(l)=number of words in S of length l. For m≤n let $\vec {a}$=(ai1,…,aim), where ik∈{1,…,n} are different; then the relative growth function with respect to $\vec {a}$ is the function Γ$\vec {a}$(l,l1,…,lm)=number of words in S of length l+l1+…+lm having (for each k) lk total occurrences of aik and aik−1.