Abstract
The paper presents a method of composing finite distributive lattices from smaller pieces and applies this to construct the finitely generated free distributive lattices from appropriate Boolean parts.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Data Availability
All datasets produced for this research as well as the software developed for that purpose are available from the author on request.
References
Balbes, R., Dwinger, P. h.: Distributive Lattices. University of Missouri Press, Columbia (1974)
Berman, J., Köhler, P.: Cardinalities of finite distributive lattices. Mitteilungen aus dem Mathem. Seminar Giessen 121, 103–124 (1976). (online: https://oeis.org/A006356/a006356.pdf)
Birkhoff, G.: Lattice Theory. Amer. Math. Soc. Coll. Publ., 3rd edn, vol. 25. Providence R.I. (1967)
Chen, C. C., Grätzer, G.: Stone lattices I. Construction Theorems. Canad. J. Math. 21, 884–894 (1969)
Chen, C. C., Grätzer, G.: Stone lattices II. Structure Theorems. Canad. J. Math. 21, 895–903 (1969)
Grätzer, G.: General Lattice Theory. Academic Press, New York-San Francisco (1978)
Köhler, P.: Quasi-decompositions of semigroups. Houst. J. Math. 5, 525–542 (1979)
Köhler, P.: The triple method and free distributive pseudocomplemted lattices. Algebra Universalis 8, 139–150 (1978)
Schmidt, J.: Quasi-decompositions, exact sequences and triple sums of semigroups I. General Theory. Contributions to Universal Algebra, Szeged. Coll. Math. Soc. Janos Bolyai 17, 365–397 (1975)
Schmidt, J.: Quasi-decompositions, exact sequences and triple sums of semigroups II. Applications. Contributions to Universal Algebra, Szeged. Coll. Math. Soc. Janos Bolyai 17, 399–428 (1975)
Wiedemann, D.: A computation of the eighth Dedekind number. Order 8, 5–6 (1991)
Acknowledgements
Thanks are due to Joel Berman for many valuable comments on earlier versions of this paper.
Funding
Open Access funding enabled and organized by Projekt DEAL.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of Interests
The author declares that he has no conflict of interest.
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Köhler, P. The Central Decomposition of FD01(n). Order 39, 159–169 (2022). https://doi.org/10.1007/s11083-021-09572-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11083-021-09572-5