Is there any formula or counting algorithm for the number of non-isomorphic posets (defined on finite n-element set)? I'm interested how to solve task *5, p.4 in Birkhoff's "Lattice Theory" the book Thanks in advance.
2026-04-07 15:28:53.1775575733
Non-isomorphic posets
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As Jair Taylor notes, the known values (which is up to $n=16$) are listed in OEIS A000112.
As for formula or algorithm: No simple formula is known. The Brinkmann & MacKay paper (2002), cited in the OEIS entry, describes an algorithm. Basically it relies on isomorph-free generation of the posets, but see the paper for details.