N -ARY OPERATIONS WITH LONG PRE-PERIODS
Klaus Denecke, Ch. Ratanaprasert · Asian-European Journal of Mathematics · 2009
Iterating a unary operation f defined on the finite set A with |A| = k one obtains the descending chain [Formula: see text] The least integer λ(f) with Imfλ(f) = Imfλ(f)+1 is called the pre-period of f. The pre-period of f is an integer between 0 and k - 1. If λ(f) = k - 1 and k ≥ 1, then f is called a long-tailed (LT)-operation and if λ(f) = k - 2 for k ≥ 2, f is said to be an (LT1)-operation. Unary (LT)- and (LT1)-operations and their invariant equivalence relations are characterized in [5]. In [6] these results are extended to partial operations. In this paper we consider the iteration of n-ary operations for n > 1, define and characterize (LT)- and (LT1)- operations and their invariant equivalence relations. The results can be applied in all fields where iteration and recursion plays a role.