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A327438
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Irregular triangle read by rows with trailing zeros removed where T(n,k) is the number of unlabeled antichains of nonempty subsets of {1..n} with spanning edge-connectivity k.
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2
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1, 1, 1, 3, 1, 6, 2, 1, 15, 7, 5, 2, 52, 53, 62, 31, 9, 1, 1
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history;
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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.
The spanning edge-connectivity of a set-system is the minimum number of edges that must be removed (without removing incident vertices) to obtain a set-system that is disconnected or covers fewer vertices.
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LINKS
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EXAMPLE
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Triangle begins:
1
1 1
3 1
6 2 1
15 7 5 2
52 53 62 31 9 1 1
The antichains counted in row n = 4 are the following:
0 {1234} {12}{134}{234} {123}{124}{134}{234}
{1} {12}{134} {123}{124}{134} {12}{13}{14}{23}{24}{34}
{12} {123}{124} {12}{13}{24}{34}
{123} {12}{13}{14} {12}{13}{14}{234}
{1}{2} {12}{13}{24} {12}{13}{14}{23}{24}
{1}{23} {12}{13}{234}
{12}{13} {12}{13}{14}{23}
{1}{234}
{12}{34}
{1}{2}{3}
{1}{2}{34}
{2}{13}{14}
{12}{13}{23}
{1}{2}{3}{4}
{4}{12}{13}{23}
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CROSSREFS
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KEYWORD
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nonn,tabf,more
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AUTHOR
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STATUS
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approved
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