期刊
DISCRETE MATHEMATICS
卷 341, 期 6, 页码 1749-1754出版社
ELSEVIER SCIENCE BV
DOI: 10.1016/j.disc.2018.03.010
关键词
05D05; Intersecting families; Erdos-Ko-Rado; Hilton-Milner; Shifting technique; Injective proof
类别
资金
- Simons Foundation [246436]
A set system F is intersecting if for any F, F' epsilon F boolean AND F' not equal (sic). A fundamental theorem of Erdos, Ko and Rado states that if F is an intersecting family of r-subsets of [n] = {1, ..., n}, and n >= 2r, then vertical bar F vertical bar <= ((n-1)(r-1)). Furthermore, when n > 2r, equality holds if and only F is the family of all r-subsets of [n] containing a fixed element. This was proved as part of a stronger result by Hilton and Milner. In this note, we provide new injective proofs of the Erdos-Ko-Rado and the Hilton-Milner theorems. (C) 2018 Elsevier B.V. All rights reserved.
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