MonotoneHurwitzNumber on IntegerPartition
The monotone factorizations of genus zero of a permutation of this cycle type into transpositions: the product of the Catalan numbers C(p - 1) over the parts p.
The cycles factor independently, and the larger entries of the transpositions, weakly increasing, fix how the factors interleave.
Called as CombinatorialStat(x, "MonotoneHurwitzNumber"). 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 St001934
The number of monotone factorisations of genus zero of a permutation of given cycle type.
| Object | Value |
|---|---|
[1] | 1 |
[2] | 1 |
[3] | 2 |
[4] | 5 |
[5] | 14 |
[6] | 42 |
[7] | 132 |
[1,1] | 1 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001934 has the rest.