  Motivation coming from the study of affine Weyl groups, a structure of ranked
poset is defined on the set of circular permutations in $S_n$ (that is,
$n$-cycles). It is isomorphic to the poset of so-called admitted vectors, and
to an interval in the affine symmetric group $\tilde S_n$ with the weak order.
The poset is a semidistributive lattice, and the rank function, whose range is
cubic in $n$, is computed by some special formula involving inversions. We
prove also some links with Eulerian numbers, triangulations of an $n$-gon, and
Young's lattice.
