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%I #10 Nov 26 2023 08:39:01
%S 1,1,3,14,146,6311,2302155
%N Number of inequivalent strict interval closure operators on a set of n elements.
%C A closure operator cl is strict if {} is closed, i.e., cl({})={}; it is interval closure operator if for every set S, the statement that for all x,y in S, cl({x,y}) is a subset of S implies that S is closed.
%C a(n) is also the number of interval convexities on a set of n elements (see Chepoi).
%D B. Ganter and R. Wille, Formal Concept Analysis - Mathematical Foundations, Springer, 1999, pages 1-15.
%H Victor Chepoi, <a href="https://www.researchgate.net/publication/2407147_Separation_Of_Two_Convex_Sets_In_Convexity_Structures">Separation of Two Convex Sets in Convexity Structures</a>
%H Dmitry I. Ignatov, <a href="https://github.com/dimachine/StrictIntervalClosures/">Supporting iPython code for counting (inequivalent) strict interval closure operators up to n=6</a>, Github repository.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Closure_operator">Closure operator</a>
%e The a(2) = 3 set-systems include {}{12}, {}{1}{2}{12}, {}{1}{12} (equivalent to {}{2}{12}).
%e The a(3) = 14 set-systems are the following (system {{}, {1,2,3}}, and sets {} and {1,2,3} are omitted).
%e {1}
%e {1}{12}
%e {12}
%e {1}{12}{13}
%e {1}{2}
%e {1}{2}{12}
%e {1}{2}{3}{12}
%e {1}{2}{3}
%e {1}{2}{13}
%e {1}{2}{3}{13}{23}
%e {1}{2}{12}{23}
%e {1}{23}
%e {1}{2}{3}{12}{13}{23}.
%Y Cf. A364656 (all strict interval closure families), A334255, A358144, A358152, A356544.
%K nonn,hard,more
%O 0,3
%A _Dmitry I. Ignatov_, Nov 18 2023
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