Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001079
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Mapping
St001079: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => 0
[1,2] => 0
[2,1] => 1
[1,2,3] => 0
[1,3,2] => 1
[2,1,3] => 1
[2,3,1] => 2
[3,1,2] => 2
[3,2,1] => 3
[1,2,3,4] => 0
[1,2,4,3] => 2
[1,3,2,4] => 1
[1,3,4,2] => 3
[1,4,2,3] => 3
[1,4,3,2] => 4
[2,1,3,4] => 1
[2,1,4,3] => 1
[2,3,1,4] => 2
[2,3,4,1] => 4
[2,4,1,3] => 2
[2,4,3,1] => 4
[3,1,2,4] => 2
[3,1,4,2] => 2
[3,2,1,4] => 3
[3,2,4,1] => 3
[3,4,1,2] => 3
[3,4,2,1] => 4
[4,1,2,3] => 4
[4,1,3,2] => 4
[4,2,1,3] => 3
[4,2,3,1] => 3
[4,3,1,2] => 4
[4,3,2,1] => 4
[1,2,3,4,5] => 0
[1,2,3,5,4] => 6
[1,2,4,3,5] => 2
[1,2,4,5,3] => 6
[1,2,5,3,4] => 6
[1,2,5,4,3] => 7
[1,3,2,4,5] => 5
[1,3,2,5,4] => 1
[1,3,4,2,5] => 5
[1,3,4,5,2] => 6
[1,3,5,2,4] => 3
[1,3,5,4,2] => 7
[1,4,2,3,5] => 5
[1,4,2,5,3] => 3
[1,4,3,2,5] => 5
[1,4,3,5,2] => 6
[1,4,5,2,3] => 5
Description
The minimal length of a factorization of a permutation using the permutations (12)(34)..., (23)(45)..., and (12). In symbols, for a permutation $\pi$ this is $$\min\{ k \mid \pi = \tau_{i_1} \cdots \tau_{i_k} \},$$ where, with $m_1$ the largest even number at most $n$ and $m_2$ the largest odd number at most $n$, each factor $\tau_i$ is one of the three permutations $(1,2)(3,4)\cdots(m_1-1,m_1)$ or $(2,3)(4,5)\cdots(m_2-1,m_2)$ or $(1,2)$.