BreakpointGraphCycles on Permutation

The alternating cycles of the breakpoint graph on 0, ..., n: a black edge from p(i) to p(i-1) and a grey edge from i to i+1, indices cyclic.

On Permutation

Each cycle of the black-then-grey successor is one alternating cycle.

Called as CombinatorialStat(x, "BreakpointGraphCycles"). The head's page has its examples.

Live

Distribution

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Sizes 1 to

FindStat St000696

The number of cycles in the breakpoint graph of a permutation.

Object	Value
[1]	2
[1,2]	3
[2,1]	1
[1,2,3]	4
[1,3,2]	2
[2,1,3]	2
[2,3,1]	2
[3,1,2]	2

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000696 has the rest.