THE ITERATION OF A BIJECTIVE TRANSFORMATION OF INTEGER K-TUPLES MOD M

For the transformation y1 = x2 +...+ x(k), y2 = x1 + x3 +...+ x(k),...,y(k) = x1 +...+ x(k-1), the possible cycle lengths and explict formulae for the number of unordered k-tuples [resp. ordered k-tuples] mod m of a given length are given and some conjectures of Stein and Everett concerning ordered k-tuples mod m are proved.