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A326573
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Number of connected antichains of subsets of {1..n}, all having different sums.
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5
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OFFSET
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0,4
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COMMENTS
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An antichain is a finite set of finite sets, none of which is a subset of any other. It is covering if its union is {1..n}. The edge-sums are the sums of vertices in each edge, so for example the edge sums of {{1,3},{2,5},{3,4,5}} are {4,7,12}.
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LINKS
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EXAMPLE
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The a(3) = 5 antichains:
{{1,2,3}}
{{1,3},{2,3}}
{{1,2},{2,3}}
{{1,2},{1,3}}
{{1,2},{1,3},{2,3}}
The a(4) = 59 antichains:
{1234} {12}{134} {12}{13}{14} {12}{13}{14}{24} {12}{13}{14}{24}{34}
{12}{234} {12}{13}{24} {12}{13}{14}{34} {12}{13}{23}{24}{34}
{13}{124} {12}{13}{34} {12}{13}{23}{24}
{13}{234} {12}{14}{34} {12}{13}{23}{34}
{14}{123} {12}{23}{24} {12}{13}{24}{34}
{14}{234} {12}{23}{34} {12}{14}{24}{34}
{23}{124} {12}{24}{34} {12}{23}{24}{34}
{23}{134} {13}{14}{24} {13}{14}{24}{34}
{24}{134} {13}{23}{24} {13}{23}{24}{34}
{34}{123} {13}{23}{34} {12}{13}{14}{234}
{123}{124} {13}{24}{34} {12}{23}{24}{134}
{123}{134} {14}{24}{34} {123}{124}{134}{234}
{123}{234} {12}{13}{234}
{124}{134} {12}{14}{234}
{124}{234} {12}{23}{134}
{134}{234} {12}{24}{134}
{13}{14}{234}
{13}{23}{124}
{14}{34}{123}
{23}{24}{134}
{12}{134}{234}
{13}{124}{234}
{14}{123}{234}
{23}{124}{134}
{123}{124}{134}
{123}{124}{234}
{123}{134}{234}
{124}{134}{234}
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CROSSREFS
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Set partitions with different block-sums are A275780.
MM-numbers of multiset partitions with different part-sums are A326535.
Antichain covers with equal edge-sums are A326566.
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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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