Abstract A family {G} G of sets is a (n induced) copy of a poset P= (P, ) P = (P, ⩽) if there exists a bijection b: P {G} b: P → G such that p q p ⩽ q holds if and only if b (p) b (q) b (p) ⊂ b (q). The induced saturation number sat^* (n, P) sat ∗ (n, P) is the minimum size of a family {F} 2^n F ⊆ 2 n that does not contain any copy of P P, but for any G 2^n {F} G ∈ 2 n \ <
Ji et al. (Sat,) studied this question.