We calculate the number of unary clones (submonoids of the full
transformation monoid) containing the permutations, on an infinite base set. It
turns out that this number is quite large, on some cardinals as large as the
whole clone lattice. Moreover we find that, with one exception, even the
cardinalities of the intervals between the monoid of all permutations and the
maximal submonoids of the full transformation monoid are as large. Whether or
not the only exception is of the same cardinality as the other intervals
depends on additional axioms of set theory.Comment: 6 page
