Induced and non-induced poset saturation problems
A subfamily G ⊆ F ⊆ 2 [ n ] of sets is a non-induced (weak) copy of a poset P in F if there exists a bijection i : P → G such that p ≤ P q implies i ( p ) ⊆ i ( q ) . In the case where in addition p ≤ P q holds if and only if i ( p ) ⊆ i ( q ) , then is an induced (strong) copy of P in G . We consider the minimum number sat ( n , P ) [resp. sat ⁎ ( n , P ) ] of sets that a family F ⊆ 2 [ n ] can have without containing a non-induced [induced] copy of P and being maximal with respect to this property, i.e., the addition of any G ∈ 2 [ n ] ∖ F creates a non-induced [induced] copy of P.
97 MATHEMATICS AND COMPUTING↗