European Journal of CombinatoricsVolume 29, Issue 1, January 2008, Pages 273-285Brace–Daykin type inequalities for intersecting familiesAuthor links open overlay panelNorihide TokushigeShow moreShareCitehttps://doi.org/10.1016/j.ejc.2006.09.001Get rights and contentUnder an Elsevier user licenseopen archiveAbstractLet n,k and r≥8 be positive integers. Suppose that a family ℱ⊂[n]k satisfies F1∩⋯∩Fr≠0̸ for all F1,…,Fr∈ℱ and ⋂F∈ℱF=0̸. We prove that there exist ϵr>0 and nr such that |ℱ|≤(r+1)n−r−1k−r+n−r−1k−r−1 holds for all n and k, satisfying n>nr and |kn−12|<ϵr.Previous article in issueNext article in issueRecommended articlesCited by (0)Copyright © 2006 Elsevier Ltd. All rights reserved.