# A computation of the eighth Dedekind number

@article{Wiedemann1991ACO, title={A computation of the eighth Dedekind number}, author={Douglas H. Wiedemann}, journal={Order}, year={1991}, volume={8}, pages={5-6} }

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.

## 70 Citations

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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.