Integer partitions and the Sperner property

The objectives of this paper are three-fold. First, we would like to call attention to a very attractive problem, the question of whether or not the poset of integer partitions ordered by re&nement has the Sperner property. We provide all necessary de&nitions, and enough bibliography to interest a newcomer in the problem. Second, we prove four new theorems, two by exhaustive computation and two in the more traditional manner. Finally, we highlight the central role played by Larry Harper in the literature of this subject. c © 2003 Elsevier B.V. All rights reserved.