{-1,2}-hypomorphy and hereditary hypomorphy coincide for posets

Authors

  • Youssef Boudabbous
  • Hamza Si Kaddour

DOI:

https://doi.org/10.11575/cdm.v4i1.61995

Abstract

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,|V|-1}, 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.

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Published

2009-06-08

Issue

Vol. 4 No. 1 (2009)

Section

Articles

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