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A computation of the eighth Dedekind number

Order volume 8, pages 5–6 (1991)Cite this article

Abstract

We compute the eighth Dedekind number, or the number of monotone collections of subsets of a set with eight elements. The number obtained is 56, 130, 437, 228, 687, 557, 907, 788.

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References

  1. J.Berman and P.Köhler (1976) Cardinalities of finite distributive lattices, Mitt. Math. Sem. Griessen 121, 103–124.

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  2. GarrettBirkhoff (1967) Lattice Theory, Amer. Math. Soc., Providence, third ed.

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  3. R.Church (1965) Enumeration by rank of the free distributive lattice with 7 generators, Notices Amer. Math. Soc. 11, 724.

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  4. A. D.Korshunov (1981) Probl. Kibern. 38, 5–108.

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Authors and Affiliations

  1. Thinking Machines Corporation, 245 First Street, 02142, Cambridge, Massachusetts, USA

    Doug Wiedemann

Authors
  1. Doug Wiedemann
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Additional information

Communicated by I. Rival

Work done while the author was with IDA-CCR, Princeton, New Jersey.

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Wiedemann, D. A computation of the eighth Dedekind number. Order 8, 5–6 (1991). https://doi.org/10.1007/BF00385808

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  • DOI: https://doi.org/10.1007/BF00385808

AMS subject classification (1991)

  • 06D99

Key words

  • Dedekind number
  • free distributive lattice
  • monotone