English

Families intersecting on an interval

Combinatorics 2007-10-10 v1

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'.

Keywords

Cite

@article{arxiv.0710.1797,
  title  = {Families intersecting on an interval},
  author = {Paul A. Russell},
  journal= {arXiv preprint arXiv:0710.1797},
  year   = {2007}
}

Comments

7 pages

R2 v1 2026-06-21T09:29:07.835Z