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

### Marina Semenova , Anna Zamojska-Dzienio

#### Abstract

We find a syntactic characterization of the class \$\\textbackslash\mathrm\\\textbackslash\mathbf\SUB\$\\textbackslash\mathcal\S$\\textbackslash\cap\\textbackslash\mathrm\Fin\\$ 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 \$\\textbackslash\mathrm\\\textbackslash\mathbf\SUB\$\\textbackslash\mathcal\S$\\textbackslash\cap\\textbackslash\mathrm\Fin\\$ forms a pseudovariety.
 Author Marina Semenova Marina Semenova,, - , Anna Zamojska-Dzienio ZATO Anna Zamojska-Dzienio,, - Department of Analysis and Sigularity Theory Journal series Order, ISSN 0167-8094, 1572-9273 Issue year 2011 Vol 28 No 3 Pages 523-548 Keywords in English 06A05, 06B05, 06B15, 06B20, 08C15, Convex, Convex and Discrete Geometry, Embedding, Geometry, Join-semidistributive, Lattice, N-free, Poset, Theory of Computation, Tree-like, Variety DOI DOI:10.1007/s11083-010-9189-6 URL http://link.springer.com/article/10.1007/s11083-010-9189-6 Score (nominal) 0 Citation count* 0 (2014-12-28)
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