论文信息 - A short proof of the existence of k-saturated partitions of partially ordered sets

A short proof of the existence of k-saturated partitions of partially ordered sets

Abstract The theorem of Greene and Kleitman concerning the existence of k -saturated partitions for any partially ordered set P is proved by applying Dilworth's theorem to the product partial order of P with a chain of length k .

Michael Saks

[1] Curtis Greene. Some Partitions Associated with a Partially Ordered Set , 1976, J. Comb. Theory, Ser. A.

[2] R. P. Dilworth,et al. A DECOMPOSITION THEOREM FOR PARTIALLY ORDERED SETS , 1950 .

[3] Alan J. Hoffman,et al. On partitions of a partially ordered set , 1977, J. Comb. Theory, Ser. B.

[4] Daniel J. Kleitman,et al. The Structure of Sperner k-Families , 1976, J. Comb. Theory, Ser. A.