The maximal clones on countable sets that include all permutations

Abstract.

We classify those maximal (also called precomplete) clones on a countably infinite base set that contain all permutations. By a result of Gavrilov's, two of them include all unary functions. The others can be represented in the form $Pol(mathcal{M})$ for countably many monoids $\mathcal{M}$ of unary functions. We give an explicit description of these monoids.