Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001938
Mapping
St001938: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1]
 => 1
[2]
 => 1
[1,1]
 => 1
[3]
 => 2
[2,1]
 => 4
[1,1,1]
 => 8
[4]
 => 5
[3,1]
 => 15
[2,2]
 => 18
[2,1,1]
 => 48
[1,1,1,1]
 => 144
[5]
 => 14
[4,1]
 => 56
[3,2]
 => 72
[3,1,1]
 => 240
[2,2,1]
 => 288
[2,1,1,1]
 => 1056
[1,1,1,1,1]
 => 4224
[6]
 => 42
[5,1]
 => 210
[4,2]
 => 280
[4,1,1]
 => 1120
[3,3]
 => 300
[3,2,1]
 => 1440
[3,1,1,1]
 => 6240
[2,2,2]
 => 1728
[2,2,1,1]
 => 7488
[2,1,1,1,1]
 => 34944
[1,1,1,1,1,1]
 => 174720
[7]
 => 132
[6,1]
 => 792
[5,2]
 => 1080
[5,1,1]
 => 5040
[4,3]
 => 1200
[4,2,1]
 => 6720
[4,1,1,1]
 => 33600
[3,3,1]
 => 7200
[3,2,2]
 => 8640
[3,2,1,1]
 => 43200
[3,1,1,1,1]
 => 230400
[2,2,2,1]
 => 51840
[2,2,1,1,1]
 => 276480
[2,1,1,1,1,1]
 => 1566720
[1,1,1,1,1,1,1]
 => 9400320
[8]
 => 429
[7,1]
 => 3003
[6,2]
 => 4158
[6,1,1]
 => 22176
[5,3]
 => 4725
[5,2,1]
 => 30240
Description
The number of transitive monotone factorizations of genus zero of a permutation of given cycle type. Let $\pi$ be a permutation of cycle type $\mu$. A transitive monotone factorisation of genus zero of a permutation $\pi\in\mathfrak S_n$ is a tuple of $r = n + \ell(\mu) - 2$ transpositions $$ (a_1, b_1),\dots,(a_r, b_r) $$ with $b_1 \leq \dots \leq b_r$ and $a_i < b_i$ for all $i$, such that the subgroup of $\mathfrak S_n$ generated by the transpositions acts transitively on $\{1,\dots,n\}$ and hose product, in this order, is $\pi$.