On Some Closed Classes of Self-dual Partial Many-valued Functions

Let $S$ be a class of fully defined functions of any number of variables that are defined and take values in the set $E_k=\{0,1,\dots,k-1\}$ and are self-dual under given permutation on $E_k$. Let $S^*$ be the set of all partially defined $k$-valued functions that can be extended to functions from $S$. In this paper all closed classes (under superposition) that contain $S$ and are contained in $S^*$ are described for the case when permutation is the product of non-intersecting cycles of the same length.