Clones of Pivotally Decomposable Functions

This paper is a contribution to the understanding of the relation between pivotal decompositions of operations on a set and clones on the same set. In this preliminary study we establish sufficient conditions on a pivotal operation II so that the corresponding class of II decomposable operations constitutes a clone, and discuss the normal form representations that such pivotal operations induce. We also outline several open questions, providing directions for further research.