On systems of finite sets with constraints on their unions and intersections |
| |
Authors: | Da-Lun Wang |
| |
Affiliation: | Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506 USA |
| |
Abstract: | Let F be a family of subsets of an n-element set. F is said to be of type (n, r, s) if A ∈ F, B ∈ F implies that |A ∪ B| ? n ? r, and |A ∩ B| ? s. Let f(n, r, s) = max {|F| : F is of type (n, r, s)}. We prove that f(n, r, s) ? f(n ? 1, r ? 1, s) + f(n ? 1, r + 1, s) if r > 0, n > s. And this result is used to give simple and unified proofs of Katona's and Frankl's results on f(n, r, s) when s = 0 and s = 1. |
| |
Keywords: | |
本文献已被 ScienceDirect 等数据库收录! |
|