On a problem of Katona on minimal completely separating systems with restrictions |
| |
Authors: | Cai Mao-cheng |
| |
Affiliation: | Institute of Systems Science, Academia Sinica, Peking 100080, China |
| |
Abstract: | Let S be a set of n elements, and k a fixed positive integer . Katona's problem is to determine the smallest integer m for which there exists a family = {A1, …, Am} of subsets of S with the following property: |i| ? k (i = 1, …, m), and for any ordered pair xi, xi ∈ S (i ≠ j) there is A1 ∈ such that xi ∈ A1, xj ? A1. It is given in this note that . |
| |
Keywords: | |
本文献已被 ScienceDirect 等数据库收录! |
|