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doi:10.1016/j.disc.2005.11.007 
Copyright © 2005 Elsevier B.V. All rights reserved.
An Erdős–Ko–Rado theorem for partial permutations
Received 20 April 2004;
revised 19 November 2005;
accepted 22 November 2005.
Available online 4 January 2006.
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Abstract
Let [n] denote the set of positive integers {1,2,…,n}. An r-partial permutation of [n] is a pair (A,f) where A
[n], |A|=r and f:A→[n] is an injective map. A set of r-partial permutations is intersecting if for any (A,f),
, there exists x
A∩B such that f(x)=g(x). We prove that for any intersecting family of r-partial permutations, we have
.
It seems rather hard to characterize the case of equality. For 8
rn-3, we show that equality holds if and only if there exist x0 and ε0 such that consists of all (A,f) for which x0
A and f(x0)=ε0.
Keywords: Intersecting families; Erdős–Ko–Rado; Permutations; Partial permutations
