The maximal clones on countable sets that include all permutations. (Q1771946)

It was recently shown by M.\ Goldstern and S.\ Shelah that the lattice of clones on an infinite (countable) set \(X\) is not dually atomic. The author classifies those maximal clones on \(X\) that contain all permutations. By G.\ P.\ Gavrilov, two of them include all unary functions. The others are represented in the form \(\text{Pol}(M)\) for countably unary monoids \(M\) of unary functions. The paper contains an explicit description of these monoids.