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Posets on up to 16 points. (English) Zbl 1006.06003
Summary: We describe a very efficient method to construct pairwise non-isomorphic posets (equivalently, \(T_0\) topologies). We also give the results obtained by a computer program based on this algorithm, in particular the numbers of non-isomorphic posets on 15 and 16 points and the numbers of labelled posets and topologies on 17 and 18 points.

MSC:
06A07 Combinatorics of partially ordered sets
06A11 Algebraic aspects of posets
05A15 Exact enumeration problems, generating functions
06-04 Software, source code, etc. for problems pertaining to ordered structures
54D10 Lower separation axioms (\(T_0\)–\(T_3\), etc.)
Software:
nauty
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