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3-Interval irreducible partially ordered sets

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Abstract

In this paper we discuss the characterization problem for posets of interval dimension at most 2. We compile the minimal list of forbidden posets for interval dimension 2. Members of this list are called 3-interval irreducible posets. The problem is related to a series of characterization problems which have been solved earlier. These are: The characterization of planar lattices, due to Kelly and Rival [5], the characterization of posets of dimension at most 2 (3-irreducible posets) which has been obtained independently by Trotter and Moore [8] and by Kelly [4] and the characterization of bipartite 3-interval irreducible posets due to Trotter [9].

We show that every 3-interval irreducible poset is a reduced partial stack of some bipartite 3-interval irreducible poset. Moreover, we succeed in classifying the 3-interval irreducible partial stacks of most of the bipartite 3-interval irreducible posets. Our arguments depend on a transformationP →B(P), such that IdimP=dimB(P). This transformation has been introduced in [2].

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Authors and Affiliations

  1. Fachbereich Mathematik, Institut für Informatik, Freie Universität Berlin, Takustr. 9, 14195, Berlin, Germany

    Stefan Felsner

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  1. Stefan Felsner
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Communicated by W. T. Trotter

Supported by the DFG under grant FE 340/2–1.

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Felsner, S. 3-Interval irreducible partially ordered sets. Order 11, 97–125 (1994). https://doi.org/10.1007/BF01108596

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  • DOI: https://doi.org/10.1007/BF01108596

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