We say that a set system F subset of 2([n]) shatters a given set S subset of [n] if 2(S) = {F boolean AND S: F is an element of F}. The Sauer-Shelah lemma states that in general, a set system F shatters at least vertical bar F vertical bar sets. We concentrate on the case of equality and call a set system shattering-extremal if it shatters exactly vertical bar F vertical bar sets. Here we discuss an approach to study these systems using Sperner families and prove some preliminary results based on an earlier algebraic approach. (C) 2019 Elsevier B.V. All rights reserved
