Order

, Volume 11, Issue 4, pp 317–341

Towards the reconstruction of posets

  • Dieter Kratsch
  • Jean-Xavier Rampon
Article

DOI: 10.1007/BF01108765

Cite this article as:
Kratsch, D. & Rampon, JX. Order (1994) 11: 317. doi:10.1007/BF01108765

Abstract

The reconstruction conjecture for posets is the following: “Every finite posetP of more than three elements is uniquely determined — up to isomorphism — by its collection of (unlabelled) one-element-deleted subposets 〈P−{x}:xV(P)〉.”

We show that disconnected posets, posets with a least (respectively, greatest) element, series decomposable posets, series-parallel posets and interval orders are reconstructible and that N-free orders are recognizable.

We show that the following parameters are reconstructible: the number of minimal (respectively, maximal) elements, the level-structure, the ideal-size sequence of the maximal elements, the ideal-size (respectively, filter-size) sequence of any fixed level of the HASSE-diagram and the number of edges of the HASSE-diagram.

This is considered to be a first step towards a proof of the reconstruction conjecture for posets.

Mathematics Subject Classification (1991)

06A07

Key words

ReconstructionKelly lemmareconstructible parameterclasses of posets

Copyright information

© Kluwer Academic Publishers 1994

Authors and Affiliations

  • Dieter Kratsch
    • 1
  • Jean-Xavier Rampon
    • 2
  1. 1.Fakultät für Mathematik und InformatikF.-Schiller-UniversitätJenaGermany
  2. 2.IRISARennes CédexFrance