Canonizing ordering theorems for Hales Jewett structures (Q1068858)

Let A be a finite set and n be a positive integer. The n-dimensional cube \(A^ n\) over A is the set of all words of length n with entries from A. The authors study the natural linear orderings of \(A^ n\). They obtain a characterization theorem for these orderings extending their earlier results [Rend. Circ. Mat. Palermo, II. Ser. Suppl. 2, 193-197 (1982; Zbl 0521.06003)]. The paper contains a detailed discussion and complete proofs of results announced in a previous paper [ibid., Suppl. 3, 191-196 (1984)].