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, Volume 11, Issue 4, pp 317-341

First online:

Towards the reconstruction of posets

  • Dieter KratschAffiliated withFakultät für Mathematik und Informatik, F.-Schiller-Universität
  • , Jean-Xavier RamponAffiliated withIRISA

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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

Reconstruction Kelly lemma reconstructible parameter classes of posets