On the Generation of (Minimal) Clones Containing Near-Unanimity Operations.

For a clone $C$ that contains a near-unanimity operation, one can define $\lambda(C)$ and $\mu(C)$ to be the smallest integers $k_1$ and $k_2$ such that $C$ is generated by its $k_1$-ary part and can be written as the set of polymorphisms of its $k_2$-th graphic, respectively. In this paper, we discuss the meaning of the functions $\lambda$ and $\mu$, elaborate the connection between them, derive some (sharp) bounds, and calculate the functions values for some selected (minimal) clones. [ABSTRACT FROM PUBLISHER]