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On Lattices Embeddable into Lattices of Order-Convex Sets. II Star-like Posets

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Abstract

We find a syntactic characterization of the class \(\mathrm{\mathbf{SUB}}(\mathcal{S})\cap\mathrm{Fin}\) of finite lattices embeddable into convexity lattices of a certain class of posets which we call star-like posets and which is a proper subclass in the class of N-free posets. The characterization implies that the class \(\mathrm{\mathbf{SUB}}(\mathcal{S})\cap\mathrm{Fin}\) forms a pseudovariety.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Siberian Branch RAS, Acad. Koptyug Prosp. 4, 630090, Novosibirsk, Russia

    Marina Semenova

  2. Novosibirsk State University, Pirogova Str. 2, 630090, Novosibirsk, Russia

    Marina Semenova

  3. Faculty of Mathematics and Information Science, Warsaw University of Technology, Plac Politechniki 1, 00-661, Warsaw, Poland

    Anna Zamojska-Dzienio

Authors
  1. Marina Semenova
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  2. Anna Zamojska-Dzienio
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Corresponding author

Correspondence to Marina Semenova.

Additional information

The first author was supported by the joint DFG-RFBR grant no. 06-01-04002 and by the Presidential Grant Council of Russian Federation, Doctors of Sciences Support grant no. MD-2587.2010.1 and Scientific Schools Support grant no. NSh-3669.2010.1. The second author was supported by the Warsaw University of Technology under statutory grant no. 504G/1120/0054000.

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Semenova, M., Zamojska-Dzienio, A. On Lattices Embeddable into Lattices of Order-Convex Sets. II Star-like Posets. Order 28, 523–548 (2011). https://doi.org/10.1007/s11083-010-9189-6

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  • DOI: https://doi.org/10.1007/s11083-010-9189-6

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