An upper bound on the size of diamond-free families of sets

Studying the average number of sets from a family of subsets of [n] on a maximal chain in the Boolean lattice 2[n] has been a fruitful method. We use a partitioning of the maximal chains and introduce an induction method to show that La(n,Q2)≤(2.20711+o(1))(n⌊n/2⌋), improving on the earlier bound of (2.25+o(1))(n⌊n/2⌋) by Kramer, Martin and Young.