Abstract: We introduce a family of posets R(k,n-k) counted by binomial coefficients. The undirected Hasse diagram of R(k,n-k) is isomorphic to Young's lattice on integer partitions in a rectangle, but the orientation is different. We show that R(k,n-k) is a graded poset of height n-k containing k^{n-k} maximal chains and we derive an explicit formula for rank-selected multichains. The poset R(k,n-k) has three interesting interpretations: (1) in terms of certain zig-zag operators for posets, (2) in terms of the affine Weyl group of type C, (3) in terms of cyclic hyperplane arrangements and the m=1 amplituhedron.
