Abstract.
Let \(\langle {\mathcal{D}}, \leq \rangle\) be the ordered set of isomorphism types of finite distributive lattices, where the ordering is by embeddability. We characterize the order ideals in \(\langle {\mathcal{D}}, \leq \rangle\) that are well-quasi-ordered by embeddability, and thus characterize the members of \(\mathcal{D}\) that belong to at least one infinite anti-chain in \(\mathcal{D}\).
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Received April 3, 2007; accepted in final form September 25, 2007.
While working on this paper, the second and third authors were supported by US NSF grant DMS-0604065. The second author was also supported by the Grant Agency of the Czech Republic, grant #201/05/0002 and by the institutional grant MSM0021620839 financed by MSMT.
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Dziobiak, W., Ježek, J. & McKenzie, R. Avoidable structures, II: Finite distributive lattices and nicely structured ordered sets. Algebra univers. 60, 259–291 (2009). https://doi.org/10.1007/s00012-009-2098-0
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DOI: https://doi.org/10.1007/s00012-009-2098-0