Name
Abstract | ||
|---|---|---|
Let X = X 1 ∪ X 2 , X 1 ∩ X 2 = 0 be a partition of an n -element set. Suppose that the family F of some subsets of X satisfy the following condition: if there is an inclusion F 1 ⊈ F 2 ( F 1 , F 2 ϵ F ) in F , the difference F 2 − F 1 cannot be a subset of X 1 or X 2 . Kleitman ( Math. Z. 90 (1965), 251–259) and Katona ( Studia Sci. Math. Hungar. 1 (1966), 59–63) proved 20 years ago that | F | is at most n choose n 2 . We determine all families giving equality in this theorem. |
Year | DOI | Venue |
|---|---|---|
1986 | 10.1016/0097-3165(86)90023-3 | J. Comb. Theory, Ser. A |
Keywords | DocType | Volume |
2-part sperner family | Journal | 43 |
Issue | ISSN | Citations |
1 | Journal of Combinatorial Theory, Series A | 8 |
PageRank | References | Authors |
1.21 | 1 | 1 |