Integer partitions and the Sperner property

• Published in: Theoretical computer science Vol. 307; no. 3; pp. 515 - 529
• Main Author: Canfield, E.Rodney
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 14-10-2003; Elsevier
• Subjects: Classical combinatorial problems; Combinatorics; Combinatorics. Ordered structures; Exact sciences and technology; Graph theory; Integer partition; Matching problem; Mathematics; Sciences and techniques of general use; Sperner property; Matching problem; Sperner property; Integer partition; Order; Unimodality; Partition; Combinatorial problem; Definition; Graph theory; Properties; Integer; Play; Upper bound; Binomial coefficient; Problem; Matching task; Stirling number
• ISSN: 0304-3975; 1879-2294
• DOI: 10.1016/S0304-3975(03)00235-4

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 refinement has the Sperner property. We provide all necessary definitions, 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.