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A327426
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Number of non-connected, unlabeled, antichain covers of {1..n} (vertex-connectivity 0).
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8
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OFFSET
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0,4
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COMMENTS
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An antichain is a set of sets, none of which is a subset of any other. It is covering if there are no isolated vertices. A singleton is not considered connected.
The vertex-connectivity of a set-system is the minimum number of vertices that must be removed (along with any resulting empty edges) to obtain a non-connected set-system or singleton. Note that this means a single node has vertex-connectivity 0.
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LINKS
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FORMULA
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EXAMPLE
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Non-isomorphic representatives of the a(2) = 1 through a(5) = 23 antichains:
{1}{2} {1}{23} {1}{234} {1}{2345}
{1}{2}{3} {12}{34} {12}{345}
{1}{2}{34} {1}{2}{345}
{1}{24}{34} {1}{23}{45}
{1}{2}{3}{4} {12}{35}{45}
{1}{23}{24}{34} {1}{25}{345}
{1}{2}{3}{45}
{1}{245}{345}
{1}{2}{35}{45}
{1}{2}{3}{4}{5}
{1}{24}{35}{45}
{1}{25}{35}{45}
{12}{34}{35}{45}
{1}{24}{25}{345}
{1}{23}{245}{345}
{1}{2}{34}{35}{45}
{1}{235}{245}{345}
{1}{23}{24}{35}{45}
{1}{25}{34}{35}{45}
{1}{23}{24}{25}{345}
{1}{234}{235}{245}{345}
{1}{24}{25}{34}{35}{45}
{1}{23}{24}{25}{34}{35}{45}
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CROSSREFS
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The non-covering version is A327424 (partial sums).
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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