Families intersecting on an interval

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We shall be interested in the following Erdo{double acute}s-Ko-Rado-type question. Fix some set B ⊂ [n] = {1, 2, ..., n}. How large a subfamily A of the power set P [n] can we find such that the intersection of any two sets in A contains a cyclic translate (modulo n) of B? Chung, Graham, Frankl and Shearer have proved that, in the case where B = [t] is a block of length t, we can do no better than taking A to consist of all supersets of B. We give an alternative proof of this result, which is in a certain sense more 'direct'. © 2008 Elsevier B.V. All rights reserved.

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Russell, P. A. (2009). Families intersecting on an interval. Discrete Mathematics, 309(9), 2952–2956. https://doi.org/10.1016/j.disc.2008.07.008

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