
{1,2}hypomorphy and hereditary hypomorphy coincide for posetsAbstract: Let P and P' be two finite posets on the same vertex set V. The posets P and P' are hereditarily hypomorphic if for every subset X of V, the induced subposets P(X) and P'(X) are isomorphic. The posets P and P' are {1,2}hypomorphic if for every subset X of V, X in {2,V1}, the subposets P(X) and P'(X) are isomorphic. P. Ille and J.X. Rampon showed that if two posets P and P', with at least 4 vertices, are {1,2}hypomorphic, then P and P' are isomorphic. Under the same hypothesis, we prove that P and P' are hereditarily hypomorphic. Moreover, we characterize the pairs of hereditarily hypomorphic posets.
