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, Volume 8, Issue 1, pp 5–6 | Cite as

A computation of the eighth Dedekind number

  • Doug Wiedemann
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.

AMS subject classification (1991)

06D99 

Key words

Dedekind number free distributive lattice monotone 

References

  1. 1.
    J.Berman and P.Köhler (1976) Cardinalities of finite distributive lattices, Mitt. Math. Sem. Griessen 121, 103–124.Google Scholar
  2. 2.
    GarrettBirkhoff (1967) Lattice Theory, Amer. Math. Soc., Providence, third ed.Google Scholar
  3. 3.
    R.Church (1965) Enumeration by rank of the free distributive lattice with 7 generators, Notices Amer. Math. Soc. 11, 724.Google Scholar
  4. 4.
    A. D.Korshunov (1981) Probl. Kibern. 38, 5–108.Google Scholar

Copyright information

© Kluwer Academic Publishers 1991

Authors and Affiliations

  • Doug Wiedemann
    • 1
  1. 1.Thinking Machines CorporationCambridgeUSA

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