  In a recent work, N. Hindman, D. Strauss and L. Zamboni have shown that the
Hales-Jewett theorem can be combined with a sufficiently well behaved
homomorphisms. In this paper we will show that those combined extensions can be
made if we replace the alphabet by an increasing sequence of alphabets, infact
it holds for some Ramsey theoretic small sets. To obtained this we achieved
some interesting configurations.
