Families intersecting on an interval

2007/10/09 by Paul A. Russell, Russell, Paul A.
Mathematics · #05D05 #Advanced Topology and Set Theory #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #math.CO #msc:05D05

paper · pdf · doi:10.48550/arxiv.0710.1797

7 pages

arxiv created 2007/10/09 · openalex publication_date 2007/10/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We shall be interested in the following Erdos-Ko-Rado-type question. Fix some subset B of [n]. How large a family A of subsets of [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 is a block of length t, we can do no better than to take A to consist of all supersets of B. We give an alternative proof of this result, which is in a certain sense more 'direct'.

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