论文信息 - Strong Versions of Sperner's Theorem

Strong Versions of Sperner's Theorem

Abstract A procedure for partitioning the collection of divisors of an integer into symmetric chains is described and analyzed in detail. As a consequence, several strengthenings of Sperner's theorem are obtained. The algorithm also leads to elementary combinatorial proofs of a number of results on lattice paths and plane partitions.

Daniel J. Kleitman | Curtis Greene | D. Kleitman | C. Greene

[1] E. Sperner. Ein Satz über Untermengen einer endlichen Menge , 1928 .

[2] R. Stanley. Theory and applications of plane partitions: Part 1 , 1971 .

[3] R. Stanley. Theory and Application of Plane Partitions. Part 2 , 1971 .

[4] de Ng Dick Bruijn,et al. On the set of divisors of a number , 1951 .

[5] Daniel J. Kleitman. Some New Results on the Littlewood-Offord Problem , 1976, J. Comb. Theory, Ser. A.

[6] Daniel J. Kleitman,et al. On a lemma of Littlewood and Offord on the distribution of certain sums , 1965 .