Partitioning Boolean lattices into antichains

Let f(n) be the smallest integer t such that a poset obtained from a Boolean lattice with n atoms by deleting both the largest and the smallest elements can be partitioned into t antichains of the same size except for possibly one antichain of a smaller size. In this paper, it is shown that f(n)b n²/log n. This is an improvement of the best previously known upper bound for f(n).