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The number of unlabeled bounded Eulerian posets with n elements.
0

%I #9 Mar 31 2023 05:00:05

%S 0,1,1,0,1,0,1,0,2,0,5,0,11

%N The number of unlabeled bounded Eulerian posets with n elements.

%C A graded partially ordered set is Eulerian if every nontrivial interval has the same number of elements of even rank as of odd rank. It is bounded if it has a unique maximal and a unique minimal element.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Eulerian_poset">Eulerian poset</a>

%o (Sage) sum(1 for P in posets(n-2) if (Q := P.with_bounds()).is_graded() and Q.is_eulerian())

%K nonn,hard,more

%O 0,9

%A _Martin Rubey_, Mar 30 2023