Integer partitions and the Sperner property

Authors:
E. Rodney Canfield
Affiliations:
Department of Computer Science, University of Georgia, Athens, GA
Venue:
Theoretical Computer Science - Selected papers in honor of Lawrence Harper
Year:
2003

Citing 6
Cited 0

Matchings in the partition lattice

SIAM Journal on Discrete Mathematics
Large antichains in the partition lattice

Random Structures & Algorithms
Asymptotic enumeration methods

Handbook of combinatorics (vol. 2)
Sperner theory

Sperner theory
The size of the largest antichain in the partition lattice

Journal of Combinatorial Theory Series A
Fundamentals of Computer Alori

Fundamentals of Computer Alori

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Abstract

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.