A computation of the eighth Dedekind number

  title={A computation of the eighth Dedekind number},
  author={Douglas H. Wiedemann},
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. 
On the number of inequivalent monotone Boolean functions of 8 variables
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On partial clones containing all idempotent partial operations
  • J. Fugère, L. Haddad
  • Mathematics
    Proceedings. 1998 28th IEEE International Symposium on Multiple- Valued Logic (Cat. No.98CB36138)
  • 1998
It is shown that though the partial clone I:=/spl cap//sub a/spl isin/k/pPol {a} of all idempotent partial operations on k is contained in finitely many partial clones, it is quite hard to determine the number of all partial clones on k containing the partial clones I on k.