TopologicallyConnectedComponents on SetPartition
The topologically connected components of the arc diagram: blocks joined when an arc of one crosses an arc of the other.
FindStat's St000925. A singleton, which has no arc, is a component of its own.
Called as CombinatorialStat(x, "TopologicallyConnectedComponents"). The head's page has its examples.
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Distribution
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FindStat St000925
The number of topologically connected components of a set partition.
| Object | Value |
|---|---|
{{1,2}} | 1 |
{{1,2,3}} | 1 |
{{1},{2}} | 2 |
{{1,2,3,4}} | 1 |
{{1,2},{3}} | 2 |
{{1,3},{2}} | 2 |
{{1},{2,3}} | 2 |
{{1,2,3,4,5}} | 1 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000925 has the rest.