anti-antichains?
Brendan McKay
bdm at cs.anu.edu.au
Mon Jul 28 08:55:15 CEST 2003
Consider the following sequences (which are all the same except
for a small shift):
==================
A000372, A007153, A014466 (Dedekind numbers)
Name: Dedekind numbers: monotone Boolean functions, or nonempty
antichains of subsets of an n-set
Example: a(2)=6 antichains
{}, {{}}, {{},{1}}, {{},{2}}, {{},{1},{2}}, {{},{1},{2},{1,2}}
==================
Those aren't antichains! An antichain (in this case) is a collection
of sets of which none is a subset of another. The correct example is
{}, {{}}, {{1}}, {{2}}, {{1,2}}, {{1},{2}}
Can some kind person please submit the changes? At the same time,
the reference to D. H. Wiedemann, personal communication, can be
replaced by
D. H. Wiedemann, A computation of the eighth Dedekind number,
Order 8 (1991) 5-6.
Brendan.
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