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) less than or equal to b n(2)/log n. This is an improvement of the best previously known upper bound for f(n). (C) 2002 Elsevier Science B.V. All rights reserved.