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A367422
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Number of inequivalent strict interval closure operators on a set of n elements.
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0
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OFFSET
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0,3
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COMMENTS
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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.
a(n) is also the number of interval convexities on a set of n elements (see Chepoi).
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REFERENCES
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B. Ganter and R. Wille, Formal Concept Analysis - Mathematical Foundations, Springer, 1999, pages 1-15.
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LINKS
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EXAMPLE
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The a(2) = 3 set-systems include {}{12}, {}{1}{2}{12}, {}{1}{12} (equivalent to {}{2}{12}).
The a(3) = 14 set-systems are the following (system {{}, {1,2,3}}, and sets {} and {1,2,3} are omitted).
{1}
{1}{12}
{12}
{1}{12}{13}
{1}{2}
{1}{2}{12}
{1}{2}{3}{12}
{1}{2}{3}
{1}{2}{13}
{1}{2}{3}{13}{23}
{1}{2}{12}{23}
{1}{23}
{1}{2}{3}{12}{13}{23}.
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CROSSREFS
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KEYWORD
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nonn,hard,more
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AUTHOR
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STATUS
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approved
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