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2019 A simple proof of the Hilton–Milner theorem
Peter Frankl
Mosc. J. Comb. Number Theory 8(2): 97-101 (2019). DOI: 10.2140/moscow.2019.8.97

Abstract

Let n2k4 be integers and a family of k-subsets of {1,2,,n}. We call intersecting if FF for all F,F, and we call nontrivial if FF=. Strengthening the famous Erdős–Ko–Rado theorem, Hilton and Milner proved that ||n1k1nk1k1+1 if is nontrivial and intersecting. We provide a proof by injection of this result.

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Peter Frankl. "A simple proof of the Hilton–Milner theorem." Mosc. J. Comb. Number Theory 8 (2) 97 - 101, 2019. https://doi.org/10.2140/moscow.2019.8.97

Information

Received: 9 October 2017; Accepted: 28 May 2018; Published: 2019
First available in Project Euclid: 29 May 2019

zbMATH: 07063266
MathSciNet: MR3959877
Digital Object Identifier: 10.2140/moscow.2019.8.97

Subjects:
Primary: 05D05

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.8 • No. 2 • 2019
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