EdgeOrbitCount on IntegerPartition
Orbits of the complete graph's edges under a permutation with these cycle lengths: the sum of half the parts rounded down, plus the sum of gcd(part, part) over pairs.
Called as CombinatorialStat(x, "EdgeOrbitCount"). The head's page has its examples.
Live
Distribution
Over IntegerPartitions at each size, tallied here in your browser; sizes past 30 are not offered.
FindStat St001982
The number of orbits of the action of a permutation of given cycle type on the set of edges of the complete graph.
| Object | Value |
|---|---|
[1] | 0 |
[2] | 1 |
[3] | 1 |
[4] | 2 |
[5] | 2 |
[6] | 3 |
[7] | 3 |
[8] | 4 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001982 has the rest.