, Volume 11, Issue 4, pp 317-341

Towards the reconstruction of posets

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access

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.

Communicated by M. Pouzet
Research partly supported by DAAD.