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Your data matches 38 different statistics following compositions of up to 3 maps.
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Matching statistic: St001569
(load all 21 compositions to match this statistic)
(load all 21 compositions to match this statistic)
St001569: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,2] => 0
[2,1] => 1
[1,2,3] => 0
[1,3,2] => 1
[2,1,3] => 1
[2,3,1] => 1
[3,1,2] => 1
[3,2,1] => 1
[1,2,3,4] => 0
[1,2,4,3] => 1
[1,3,2,4] => 1
[1,3,4,2] => 2
[1,4,2,3] => 2
[1,4,3,2] => 2
[2,1,3,4] => 1
[2,1,4,3] => 1
[2,3,1,4] => 2
[2,3,4,1] => 1
[2,4,1,3] => 2
[2,4,3,1] => 2
[3,1,2,4] => 2
[3,1,4,2] => 2
[3,2,1,4] => 2
[3,2,4,1] => 2
[3,4,1,2] => 2
[3,4,2,1] => 2
[4,1,2,3] => 1
[4,1,3,2] => 2
[4,2,1,3] => 2
[4,2,3,1] => 1
[4,3,1,2] => 2
[4,3,2,1] => 1
[1,2,3,4,5] => 0
[1,2,3,5,4] => 1
[1,2,4,3,5] => 1
[1,2,4,5,3] => 2
[1,2,5,3,4] => 2
[1,2,5,4,3] => 2
[1,3,2,4,5] => 1
[1,3,2,5,4] => 1
[1,3,4,2,5] => 2
[1,3,4,5,2] => 2
[1,3,5,2,4] => 2
[1,3,5,4,2] => 2
[1,4,2,3,5] => 2
[1,4,2,5,3] => 2
[1,4,3,2,5] => 2
[1,4,3,5,2] => 2
[1,4,5,2,3] => 2
[1,4,5,3,2] => 2
Description
The maximal modular displacement of a permutation.
This is $\max_{1\leq i \leq n} \left(\min(\pi(i)-i\pmod n, i-\pi(i)\pmod n)\right)$ for a permutation $\pi$ of $\{1,\dots,n\}$.
Matching statistic: St000260
(load all 5 compositions to match this statistic)
(load all 5 compositions to match this statistic)
Values
[1,2] => ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1
[2,1] => ([],2)
=> ([],2)
=> ([],1)
=> 0
[1,2,3] => ([(0,2),(2,1)],3)
=> ([(0,2),(1,2)],3)
=> ([(0,1)],2)
=> 1
[1,3,2] => ([(0,1),(0,2)],3)
=> ([(0,2),(1,2)],3)
=> ([(0,1)],2)
=> 1
[2,1,3] => ([(0,2),(1,2)],3)
=> ([(0,2),(1,2)],3)
=> ([(0,1)],2)
=> 1
[2,3,1] => ([(1,2)],3)
=> ([(1,2)],3)
=> ([(1,2)],3)
=> ? ∊ {1,1}
[3,1,2] => ([(1,2)],3)
=> ([(1,2)],3)
=> ([(1,2)],3)
=> ? ∊ {1,1}
[3,2,1] => ([],3)
=> ([],3)
=> ([],1)
=> 0
[1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[1,2,4,3] => ([(0,3),(3,1),(3,2)],4)
=> ([(0,3),(1,3),(2,3)],4)
=> ([(0,1)],2)
=> 1
[1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> 1
[1,3,4,2] => ([(0,2),(0,3),(3,1)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[1,4,2,3] => ([(0,2),(0,3),(3,1)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[1,4,3,2] => ([(0,1),(0,2),(0,3)],4)
=> ([(0,3),(1,3),(2,3)],4)
=> ([(0,1)],2)
=> 1
[2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
=> ([(0,3),(1,3),(2,3)],4)
=> ([(0,1)],2)
=> 1
[2,1,4,3] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> 1
[2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[2,3,4,1] => ([(1,2),(2,3)],4)
=> ([(1,3),(2,3)],4)
=> ([(1,2)],3)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2}
[2,4,1,3] => ([(0,3),(1,2),(1,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[2,4,3,1] => ([(1,2),(1,3)],4)
=> ([(1,3),(2,3)],4)
=> ([(1,2)],3)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2}
[3,1,2,4] => ([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[3,1,4,2] => ([(0,3),(1,2),(1,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
=> ([(0,3),(1,3),(2,3)],4)
=> ([(0,1)],2)
=> 1
[3,2,4,1] => ([(1,3),(2,3)],4)
=> ([(1,3),(2,3)],4)
=> ([(1,2)],3)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2}
[3,4,1,2] => ([(0,3),(1,2)],4)
=> ([(0,3),(1,2)],4)
=> ([(0,3),(1,2)],4)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2}
[3,4,2,1] => ([(2,3)],4)
=> ([(2,3)],4)
=> ([(1,2)],3)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2}
[4,1,2,3] => ([(1,2),(2,3)],4)
=> ([(1,3),(2,3)],4)
=> ([(1,2)],3)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2}
[4,1,3,2] => ([(1,2),(1,3)],4)
=> ([(1,3),(2,3)],4)
=> ([(1,2)],3)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2}
[4,2,1,3] => ([(1,3),(2,3)],4)
=> ([(1,3),(2,3)],4)
=> ([(1,2)],3)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2}
[4,2,3,1] => ([(2,3)],4)
=> ([(2,3)],4)
=> ([(1,2)],3)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2}
[4,3,1,2] => ([(2,3)],4)
=> ([(2,3)],4)
=> ([(1,2)],3)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2}
[4,3,2,1] => ([],4)
=> ([],4)
=> ([],1)
=> 0
[1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 2
[1,2,3,5,4] => ([(0,3),(3,4),(4,1),(4,2)],5)
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[1,2,4,3,5] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[1,2,4,5,3] => ([(0,4),(3,2),(4,1),(4,3)],5)
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[1,2,5,3,4] => ([(0,4),(3,2),(4,1),(4,3)],5)
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[1,2,5,4,3] => ([(0,4),(4,1),(4,2),(4,3)],5)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,1)],2)
=> 1
[1,3,2,4,5] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[1,3,2,5,4] => ([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> 1
[1,3,4,2,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> 2
[1,3,4,5,2] => ([(0,2),(0,4),(3,1),(4,3)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 2
[1,3,5,2,4] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[1,3,5,4,2] => ([(0,3),(0,4),(4,1),(4,2)],5)
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[1,4,2,3,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> 2
[1,4,2,5,3] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> 1
[1,4,3,5,2] => ([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
=> ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[1,4,5,2,3] => ([(0,3),(0,4),(3,2),(4,1)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 2
[1,4,5,3,2] => ([(0,2),(0,3),(0,4),(4,1)],5)
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[1,5,2,3,4] => ([(0,2),(0,4),(3,1),(4,3)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 2
[1,5,2,4,3] => ([(0,3),(0,4),(4,1),(4,2)],5)
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[1,5,3,2,4] => ([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
=> ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[1,5,3,4,2] => ([(0,2),(0,3),(0,4),(4,1)],5)
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[1,5,4,2,3] => ([(0,2),(0,3),(0,4),(4,1)],5)
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[1,5,4,3,2] => ([(0,1),(0,2),(0,3),(0,4)],5)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,1)],2)
=> 1
[2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[2,1,3,5,4] => ([(0,4),(1,4),(4,2),(4,3)],5)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,1)],2)
=> 1
[2,1,4,3,5] => ([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> 1
[2,1,4,5,3] => ([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
=> ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[2,1,5,3,4] => ([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
=> ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[2,1,5,4,3] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> 1
[2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
=> ([(1,4),(2,3),(3,4)],5)
=> ([(1,4),(2,3),(3,4)],5)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,3,5,4,1] => ([(1,4),(4,2),(4,3)],5)
=> ([(1,4),(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,4,3,5,1] => ([(1,2),(1,3),(2,4),(3,4)],5)
=> ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,4,5,3,1] => ([(1,3),(1,4),(4,2)],5)
=> ([(1,4),(2,3),(3,4)],5)
=> ([(1,4),(2,3),(3,4)],5)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,5,3,4,1] => ([(1,3),(1,4),(4,2)],5)
=> ([(1,4),(2,3),(3,4)],5)
=> ([(1,4),(2,3),(3,4)],5)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,5,4,3,1] => ([(1,2),(1,3),(1,4)],5)
=> ([(1,4),(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,2,4,5,1] => ([(1,4),(2,4),(4,3)],5)
=> ([(1,4),(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,2,5,4,1] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,4,2,5,1] => ([(1,4),(2,3),(3,4)],5)
=> ([(1,4),(2,3),(3,4)],5)
=> ([(1,4),(2,3),(3,4)],5)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
=> ([(0,1),(2,4),(3,4)],5)
=> ([(0,3),(1,2)],4)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,4,5,2,1] => ([(2,3),(3,4)],5)
=> ([(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,5,2,4,1] => ([(1,4),(2,3),(2,4)],5)
=> ([(1,4),(2,3),(3,4)],5)
=> ([(1,4),(2,3),(3,4)],5)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,5,4,1,2] => ([(0,4),(1,2),(1,3)],5)
=> ([(0,1),(2,4),(3,4)],5)
=> ([(0,3),(1,2)],4)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,5,4,2,1] => ([(2,3),(2,4)],5)
=> ([(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[4,2,3,5,1] => ([(1,4),(2,3),(3,4)],5)
=> ([(1,4),(2,3),(3,4)],5)
=> ([(1,4),(2,3),(3,4)],5)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[4,2,5,3,1] => ([(1,4),(2,3),(2,4)],5)
=> ([(1,4),(2,3),(3,4)],5)
=> ([(1,4),(2,3),(3,4)],5)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[4,3,2,5,1] => ([(1,4),(2,4),(3,4)],5)
=> ([(1,4),(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[4,3,5,1,2] => ([(0,4),(1,4),(2,3)],5)
=> ([(0,1),(2,4),(3,4)],5)
=> ([(0,3),(1,2)],4)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[4,3,5,2,1] => ([(2,4),(3,4)],5)
=> ([(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[4,5,1,2,3] => ([(0,3),(1,4),(4,2)],5)
=> ([(0,1),(2,4),(3,4)],5)
=> ([(0,3),(1,2)],4)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[4,5,1,3,2] => ([(0,4),(1,2),(1,3)],5)
=> ([(0,1),(2,4),(3,4)],5)
=> ([(0,3),(1,2)],4)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[4,5,2,1,3] => ([(0,4),(1,4),(2,3)],5)
=> ([(0,1),(2,4),(3,4)],5)
=> ([(0,3),(1,2)],4)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[4,5,2,3,1] => ([(1,4),(2,3)],5)
=> ([(1,4),(2,3)],5)
=> ([(1,4),(2,3)],5)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[4,5,3,1,2] => ([(1,4),(2,3)],5)
=> ([(1,4),(2,3)],5)
=> ([(1,4),(2,3)],5)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[4,5,3,2,1] => ([(3,4)],5)
=> ([(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[5,1,2,3,4] => ([(1,4),(3,2),(4,3)],5)
=> ([(1,4),(2,3),(3,4)],5)
=> ([(1,4),(2,3),(3,4)],5)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[5,1,2,4,3] => ([(1,4),(4,2),(4,3)],5)
=> ([(1,4),(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[5,1,3,2,4] => ([(1,2),(1,3),(2,4),(3,4)],5)
=> ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[5,1,3,4,2] => ([(1,3),(1,4),(4,2)],5)
=> ([(1,4),(2,3),(3,4)],5)
=> ([(1,4),(2,3),(3,4)],5)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[5,1,4,2,3] => ([(1,3),(1,4),(4,2)],5)
=> ([(1,4),(2,3),(3,4)],5)
=> ([(1,4),(2,3),(3,4)],5)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[5,1,4,3,2] => ([(1,2),(1,3),(1,4)],5)
=> ([(1,4),(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[5,2,1,3,4] => ([(1,4),(2,4),(4,3)],5)
=> ([(1,4),(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[5,2,1,4,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[5,2,3,1,4] => ([(1,4),(2,3),(3,4)],5)
=> ([(1,4),(2,3),(3,4)],5)
=> ([(1,4),(2,3),(3,4)],5)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[5,2,3,4,1] => ([(2,3),(3,4)],5)
=> ([(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[5,2,4,1,3] => ([(1,4),(2,3),(2,4)],5)
=> ([(1,4),(2,3),(3,4)],5)
=> ([(1,4),(2,3),(3,4)],5)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[5,2,4,3,1] => ([(2,3),(2,4)],5)
=> ([(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[5,3,1,2,4] => ([(1,4),(2,3),(3,4)],5)
=> ([(1,4),(2,3),(3,4)],5)
=> ([(1,4),(2,3),(3,4)],5)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
Description
The radius of a connected graph.
This is the minimum eccentricity of any vertex.
Matching statistic: St000668
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00068: Permutations —Simion-Schmidt map⟶ Permutations
Mp00108: Permutations —cycle type⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000668: Integer partitions ⟶ ℤResult quality: 54% ●values known / values provided: 54%●distinct values known / distinct values provided: 67%
Mp00108: Permutations —cycle type⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000668: Integer partitions ⟶ ℤResult quality: 54% ●values known / values provided: 54%●distinct values known / distinct values provided: 67%
Values
[1,2] => [1,2] => [1,1]
=> [1]
=> ? ∊ {0,1}
[2,1] => [2,1] => [2]
=> []
=> ? ∊ {0,1}
[1,2,3] => [1,3,2] => [2,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1}
[1,3,2] => [1,3,2] => [2,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1}
[2,1,3] => [2,1,3] => [2,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1}
[2,3,1] => [2,3,1] => [3]
=> []
=> ? ∊ {0,1,1,1,1,1}
[3,1,2] => [3,1,2] => [3]
=> []
=> ? ∊ {0,1,1,1,1,1}
[3,2,1] => [3,2,1] => [2,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1}
[1,2,3,4] => [1,4,3,2] => [2,1,1]
=> [1,1]
=> 1
[1,2,4,3] => [1,4,3,2] => [2,1,1]
=> [1,1]
=> 1
[1,3,2,4] => [1,4,3,2] => [2,1,1]
=> [1,1]
=> 1
[1,3,4,2] => [1,4,3,2] => [2,1,1]
=> [1,1]
=> 1
[1,4,2,3] => [1,4,3,2] => [2,1,1]
=> [1,1]
=> 1
[1,4,3,2] => [1,4,3,2] => [2,1,1]
=> [1,1]
=> 1
[2,1,3,4] => [2,1,4,3] => [2,2]
=> [2]
=> 2
[2,1,4,3] => [2,1,4,3] => [2,2]
=> [2]
=> 2
[2,3,1,4] => [2,4,1,3] => [4]
=> []
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2}
[2,3,4,1] => [2,4,3,1] => [3,1]
=> [1]
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2}
[2,4,1,3] => [2,4,1,3] => [4]
=> []
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2}
[2,4,3,1] => [2,4,3,1] => [3,1]
=> [1]
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2}
[3,1,2,4] => [3,1,4,2] => [4]
=> []
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2}
[3,1,4,2] => [3,1,4,2] => [4]
=> []
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2}
[3,2,1,4] => [3,2,1,4] => [2,1,1]
=> [1,1]
=> 1
[3,2,4,1] => [3,2,4,1] => [3,1]
=> [1]
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2}
[3,4,1,2] => [3,4,1,2] => [2,2]
=> [2]
=> 2
[3,4,2,1] => [3,4,2,1] => [4]
=> []
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2}
[4,1,2,3] => [4,1,3,2] => [3,1]
=> [1]
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2}
[4,1,3,2] => [4,1,3,2] => [3,1]
=> [1]
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2}
[4,2,1,3] => [4,2,1,3] => [3,1]
=> [1]
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2}
[4,2,3,1] => [4,2,3,1] => [2,1,1]
=> [1,1]
=> 1
[4,3,1,2] => [4,3,1,2] => [4]
=> []
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2}
[4,3,2,1] => [4,3,2,1] => [2,2]
=> [2]
=> 2
[1,2,3,4,5] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,2,3,5,4] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,2,4,3,5] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,2,4,5,3] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,2,5,3,4] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,2,5,4,3] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,3,2,4,5] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,3,2,5,4] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,3,4,2,5] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,3,4,5,2] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,3,5,2,4] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,3,5,4,2] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,4,2,3,5] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,4,2,5,3] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,4,3,2,5] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,4,3,5,2] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,4,5,2,3] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,4,5,3,2] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,5,2,3,4] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,5,2,4,3] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,5,3,2,4] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,5,3,4,2] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,5,4,2,3] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,5,4,3,2] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[2,1,3,4,5] => [2,1,5,4,3] => [2,2,1]
=> [2,1]
=> 2
[2,1,3,5,4] => [2,1,5,4,3] => [2,2,1]
=> [2,1]
=> 2
[2,1,4,3,5] => [2,1,5,4,3] => [2,2,1]
=> [2,1]
=> 2
[2,1,4,5,3] => [2,1,5,4,3] => [2,2,1]
=> [2,1]
=> 2
[2,1,5,3,4] => [2,1,5,4,3] => [2,2,1]
=> [2,1]
=> 2
[2,1,5,4,3] => [2,1,5,4,3] => [2,2,1]
=> [2,1]
=> 2
[2,3,1,4,5] => [2,5,1,4,3] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,3,1,5,4] => [2,5,1,4,3] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,3,4,1,5] => [2,5,4,1,3] => [5]
=> []
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,3,4,5,1] => [2,5,4,3,1] => [3,2]
=> [2]
=> 2
[2,3,5,1,4] => [2,5,4,1,3] => [5]
=> []
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,3,5,4,1] => [2,5,4,3,1] => [3,2]
=> [2]
=> 2
[2,4,1,3,5] => [2,5,1,4,3] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,4,1,5,3] => [2,5,1,4,3] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,4,3,1,5] => [2,5,4,1,3] => [5]
=> []
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,4,3,5,1] => [2,5,4,3,1] => [3,2]
=> [2]
=> 2
[2,4,5,1,3] => [2,5,4,1,3] => [5]
=> []
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,4,5,3,1] => [2,5,4,3,1] => [3,2]
=> [2]
=> 2
[2,5,1,3,4] => [2,5,1,4,3] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,5,1,4,3] => [2,5,1,4,3] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,5,3,1,4] => [2,5,4,1,3] => [5]
=> []
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,5,3,4,1] => [2,5,4,3,1] => [3,2]
=> [2]
=> 2
[2,5,4,1,3] => [2,5,4,1,3] => [5]
=> []
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,5,4,3,1] => [2,5,4,3,1] => [3,2]
=> [2]
=> 2
[3,1,2,4,5] => [3,1,5,4,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,1,2,5,4] => [3,1,5,4,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,1,4,2,5] => [3,1,5,4,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,1,4,5,2] => [3,1,5,4,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,1,5,2,4] => [3,1,5,4,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,1,5,4,2] => [3,1,5,4,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,2,1,4,5] => [3,2,1,5,4] => [2,2,1]
=> [2,1]
=> 2
[3,2,1,5,4] => [3,2,1,5,4] => [2,2,1]
=> [2,1]
=> 2
[3,2,4,1,5] => [3,2,5,1,4] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,2,5,1,4] => [3,2,5,1,4] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,4,2,1,5] => [3,5,2,1,4] => [5]
=> []
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,4,2,5,1] => [3,5,2,4,1] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,4,5,2,1] => [3,5,4,2,1] => [5]
=> []
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,5,2,1,4] => [3,5,2,1,4] => [5]
=> []
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,5,2,4,1] => [3,5,2,4,1] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,5,4,2,1] => [3,5,4,2,1] => [5]
=> []
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[4,1,2,3,5] => [4,1,5,3,2] => [5]
=> []
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[4,1,2,5,3] => [4,1,5,3,2] => [5]
=> []
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[4,1,3,2,5] => [4,1,5,3,2] => [5]
=> []
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[4,1,3,5,2] => [4,1,5,3,2] => [5]
=> []
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
Description
The least common multiple of the parts of the partition.
Matching statistic: St000707
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00068: Permutations —Simion-Schmidt map⟶ Permutations
Mp00108: Permutations —cycle type⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000707: Integer partitions ⟶ ℤResult quality: 54% ●values known / values provided: 54%●distinct values known / distinct values provided: 67%
Mp00108: Permutations —cycle type⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000707: Integer partitions ⟶ ℤResult quality: 54% ●values known / values provided: 54%●distinct values known / distinct values provided: 67%
Values
[1,2] => [1,2] => [1,1]
=> [1]
=> ? ∊ {0,1}
[2,1] => [2,1] => [2]
=> []
=> ? ∊ {0,1}
[1,2,3] => [1,3,2] => [2,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1}
[1,3,2] => [1,3,2] => [2,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1}
[2,1,3] => [2,1,3] => [2,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1}
[2,3,1] => [2,3,1] => [3]
=> []
=> ? ∊ {0,1,1,1,1,1}
[3,1,2] => [3,1,2] => [3]
=> []
=> ? ∊ {0,1,1,1,1,1}
[3,2,1] => [3,2,1] => [2,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1}
[1,2,3,4] => [1,4,3,2] => [2,1,1]
=> [1,1]
=> 1
[1,2,4,3] => [1,4,3,2] => [2,1,1]
=> [1,1]
=> 1
[1,3,2,4] => [1,4,3,2] => [2,1,1]
=> [1,1]
=> 1
[1,3,4,2] => [1,4,3,2] => [2,1,1]
=> [1,1]
=> 1
[1,4,2,3] => [1,4,3,2] => [2,1,1]
=> [1,1]
=> 1
[1,4,3,2] => [1,4,3,2] => [2,1,1]
=> [1,1]
=> 1
[2,1,3,4] => [2,1,4,3] => [2,2]
=> [2]
=> 2
[2,1,4,3] => [2,1,4,3] => [2,2]
=> [2]
=> 2
[2,3,1,4] => [2,4,1,3] => [4]
=> []
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2}
[2,3,4,1] => [2,4,3,1] => [3,1]
=> [1]
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2}
[2,4,1,3] => [2,4,1,3] => [4]
=> []
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2}
[2,4,3,1] => [2,4,3,1] => [3,1]
=> [1]
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2}
[3,1,2,4] => [3,1,4,2] => [4]
=> []
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2}
[3,1,4,2] => [3,1,4,2] => [4]
=> []
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2}
[3,2,1,4] => [3,2,1,4] => [2,1,1]
=> [1,1]
=> 1
[3,2,4,1] => [3,2,4,1] => [3,1]
=> [1]
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2}
[3,4,1,2] => [3,4,1,2] => [2,2]
=> [2]
=> 2
[3,4,2,1] => [3,4,2,1] => [4]
=> []
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2}
[4,1,2,3] => [4,1,3,2] => [3,1]
=> [1]
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2}
[4,1,3,2] => [4,1,3,2] => [3,1]
=> [1]
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2}
[4,2,1,3] => [4,2,1,3] => [3,1]
=> [1]
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2}
[4,2,3,1] => [4,2,3,1] => [2,1,1]
=> [1,1]
=> 1
[4,3,1,2] => [4,3,1,2] => [4]
=> []
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2}
[4,3,2,1] => [4,3,2,1] => [2,2]
=> [2]
=> 2
[1,2,3,4,5] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,2,3,5,4] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,2,4,3,5] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,2,4,5,3] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,2,5,3,4] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,2,5,4,3] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,3,2,4,5] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,3,2,5,4] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,3,4,2,5] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,3,4,5,2] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,3,5,2,4] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,3,5,4,2] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,4,2,3,5] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,4,2,5,3] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,4,3,2,5] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,4,3,5,2] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,4,5,2,3] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,4,5,3,2] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,5,2,3,4] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,5,2,4,3] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,5,3,2,4] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,5,3,4,2] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,5,4,2,3] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,5,4,3,2] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[2,1,3,4,5] => [2,1,5,4,3] => [2,2,1]
=> [2,1]
=> 2
[2,1,3,5,4] => [2,1,5,4,3] => [2,2,1]
=> [2,1]
=> 2
[2,1,4,3,5] => [2,1,5,4,3] => [2,2,1]
=> [2,1]
=> 2
[2,1,4,5,3] => [2,1,5,4,3] => [2,2,1]
=> [2,1]
=> 2
[2,1,5,3,4] => [2,1,5,4,3] => [2,2,1]
=> [2,1]
=> 2
[2,1,5,4,3] => [2,1,5,4,3] => [2,2,1]
=> [2,1]
=> 2
[2,3,1,4,5] => [2,5,1,4,3] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,3,1,5,4] => [2,5,1,4,3] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,3,4,1,5] => [2,5,4,1,3] => [5]
=> []
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,3,4,5,1] => [2,5,4,3,1] => [3,2]
=> [2]
=> 2
[2,3,5,1,4] => [2,5,4,1,3] => [5]
=> []
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,3,5,4,1] => [2,5,4,3,1] => [3,2]
=> [2]
=> 2
[2,4,1,3,5] => [2,5,1,4,3] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,4,1,5,3] => [2,5,1,4,3] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,4,3,1,5] => [2,5,4,1,3] => [5]
=> []
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,4,3,5,1] => [2,5,4,3,1] => [3,2]
=> [2]
=> 2
[2,4,5,1,3] => [2,5,4,1,3] => [5]
=> []
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,4,5,3,1] => [2,5,4,3,1] => [3,2]
=> [2]
=> 2
[2,5,1,3,4] => [2,5,1,4,3] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,5,1,4,3] => [2,5,1,4,3] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,5,3,1,4] => [2,5,4,1,3] => [5]
=> []
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,5,3,4,1] => [2,5,4,3,1] => [3,2]
=> [2]
=> 2
[2,5,4,1,3] => [2,5,4,1,3] => [5]
=> []
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,5,4,3,1] => [2,5,4,3,1] => [3,2]
=> [2]
=> 2
[3,1,2,4,5] => [3,1,5,4,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,1,2,5,4] => [3,1,5,4,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,1,4,2,5] => [3,1,5,4,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,1,4,5,2] => [3,1,5,4,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,1,5,2,4] => [3,1,5,4,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,1,5,4,2] => [3,1,5,4,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,2,1,4,5] => [3,2,1,5,4] => [2,2,1]
=> [2,1]
=> 2
[3,2,1,5,4] => [3,2,1,5,4] => [2,2,1]
=> [2,1]
=> 2
[3,2,4,1,5] => [3,2,5,1,4] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,2,5,1,4] => [3,2,5,1,4] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,4,2,1,5] => [3,5,2,1,4] => [5]
=> []
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,4,2,5,1] => [3,5,2,4,1] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,4,5,2,1] => [3,5,4,2,1] => [5]
=> []
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,5,2,1,4] => [3,5,2,1,4] => [5]
=> []
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,5,2,4,1] => [3,5,2,4,1] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,5,4,2,1] => [3,5,4,2,1] => [5]
=> []
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[4,1,2,3,5] => [4,1,5,3,2] => [5]
=> []
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[4,1,2,5,3] => [4,1,5,3,2] => [5]
=> []
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[4,1,3,2,5] => [4,1,5,3,2] => [5]
=> []
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[4,1,3,5,2] => [4,1,5,3,2] => [5]
=> []
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
Description
The product of the factorials of the parts.
Matching statistic: St000708
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00068: Permutations —Simion-Schmidt map⟶ Permutations
Mp00108: Permutations —cycle type⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000708: Integer partitions ⟶ ℤResult quality: 54% ●values known / values provided: 54%●distinct values known / distinct values provided: 67%
Mp00108: Permutations —cycle type⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000708: Integer partitions ⟶ ℤResult quality: 54% ●values known / values provided: 54%●distinct values known / distinct values provided: 67%
Values
[1,2] => [1,2] => [1,1]
=> [1]
=> ? ∊ {0,1}
[2,1] => [2,1] => [2]
=> []
=> ? ∊ {0,1}
[1,2,3] => [1,3,2] => [2,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1}
[1,3,2] => [1,3,2] => [2,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1}
[2,1,3] => [2,1,3] => [2,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1}
[2,3,1] => [2,3,1] => [3]
=> []
=> ? ∊ {0,1,1,1,1,1}
[3,1,2] => [3,1,2] => [3]
=> []
=> ? ∊ {0,1,1,1,1,1}
[3,2,1] => [3,2,1] => [2,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1}
[1,2,3,4] => [1,4,3,2] => [2,1,1]
=> [1,1]
=> 1
[1,2,4,3] => [1,4,3,2] => [2,1,1]
=> [1,1]
=> 1
[1,3,2,4] => [1,4,3,2] => [2,1,1]
=> [1,1]
=> 1
[1,3,4,2] => [1,4,3,2] => [2,1,1]
=> [1,1]
=> 1
[1,4,2,3] => [1,4,3,2] => [2,1,1]
=> [1,1]
=> 1
[1,4,3,2] => [1,4,3,2] => [2,1,1]
=> [1,1]
=> 1
[2,1,3,4] => [2,1,4,3] => [2,2]
=> [2]
=> 2
[2,1,4,3] => [2,1,4,3] => [2,2]
=> [2]
=> 2
[2,3,1,4] => [2,4,1,3] => [4]
=> []
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2}
[2,3,4,1] => [2,4,3,1] => [3,1]
=> [1]
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2}
[2,4,1,3] => [2,4,1,3] => [4]
=> []
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2}
[2,4,3,1] => [2,4,3,1] => [3,1]
=> [1]
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2}
[3,1,2,4] => [3,1,4,2] => [4]
=> []
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2}
[3,1,4,2] => [3,1,4,2] => [4]
=> []
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2}
[3,2,1,4] => [3,2,1,4] => [2,1,1]
=> [1,1]
=> 1
[3,2,4,1] => [3,2,4,1] => [3,1]
=> [1]
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2}
[3,4,1,2] => [3,4,1,2] => [2,2]
=> [2]
=> 2
[3,4,2,1] => [3,4,2,1] => [4]
=> []
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2}
[4,1,2,3] => [4,1,3,2] => [3,1]
=> [1]
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2}
[4,1,3,2] => [4,1,3,2] => [3,1]
=> [1]
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2}
[4,2,1,3] => [4,2,1,3] => [3,1]
=> [1]
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2}
[4,2,3,1] => [4,2,3,1] => [2,1,1]
=> [1,1]
=> 1
[4,3,1,2] => [4,3,1,2] => [4]
=> []
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2}
[4,3,2,1] => [4,3,2,1] => [2,2]
=> [2]
=> 2
[1,2,3,4,5] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,2,3,5,4] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,2,4,3,5] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,2,4,5,3] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,2,5,3,4] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,2,5,4,3] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,3,2,4,5] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,3,2,5,4] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,3,4,2,5] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,3,4,5,2] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,3,5,2,4] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,3,5,4,2] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,4,2,3,5] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,4,2,5,3] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,4,3,2,5] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,4,3,5,2] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,4,5,2,3] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,4,5,3,2] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,5,2,3,4] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,5,2,4,3] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,5,3,2,4] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,5,3,4,2] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,5,4,2,3] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,5,4,3,2] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[2,1,3,4,5] => [2,1,5,4,3] => [2,2,1]
=> [2,1]
=> 2
[2,1,3,5,4] => [2,1,5,4,3] => [2,2,1]
=> [2,1]
=> 2
[2,1,4,3,5] => [2,1,5,4,3] => [2,2,1]
=> [2,1]
=> 2
[2,1,4,5,3] => [2,1,5,4,3] => [2,2,1]
=> [2,1]
=> 2
[2,1,5,3,4] => [2,1,5,4,3] => [2,2,1]
=> [2,1]
=> 2
[2,1,5,4,3] => [2,1,5,4,3] => [2,2,1]
=> [2,1]
=> 2
[2,3,1,4,5] => [2,5,1,4,3] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,3,1,5,4] => [2,5,1,4,3] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,3,4,1,5] => [2,5,4,1,3] => [5]
=> []
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,3,4,5,1] => [2,5,4,3,1] => [3,2]
=> [2]
=> 2
[2,3,5,1,4] => [2,5,4,1,3] => [5]
=> []
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,3,5,4,1] => [2,5,4,3,1] => [3,2]
=> [2]
=> 2
[2,4,1,3,5] => [2,5,1,4,3] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,4,1,5,3] => [2,5,1,4,3] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,4,3,1,5] => [2,5,4,1,3] => [5]
=> []
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,4,3,5,1] => [2,5,4,3,1] => [3,2]
=> [2]
=> 2
[2,4,5,1,3] => [2,5,4,1,3] => [5]
=> []
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,4,5,3,1] => [2,5,4,3,1] => [3,2]
=> [2]
=> 2
[2,5,1,3,4] => [2,5,1,4,3] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,5,1,4,3] => [2,5,1,4,3] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,5,3,1,4] => [2,5,4,1,3] => [5]
=> []
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,5,3,4,1] => [2,5,4,3,1] => [3,2]
=> [2]
=> 2
[2,5,4,1,3] => [2,5,4,1,3] => [5]
=> []
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,5,4,3,1] => [2,5,4,3,1] => [3,2]
=> [2]
=> 2
[3,1,2,4,5] => [3,1,5,4,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,1,2,5,4] => [3,1,5,4,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,1,4,2,5] => [3,1,5,4,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,1,4,5,2] => [3,1,5,4,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,1,5,2,4] => [3,1,5,4,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,1,5,4,2] => [3,1,5,4,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,2,1,4,5] => [3,2,1,5,4] => [2,2,1]
=> [2,1]
=> 2
[3,2,1,5,4] => [3,2,1,5,4] => [2,2,1]
=> [2,1]
=> 2
[3,2,4,1,5] => [3,2,5,1,4] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,2,5,1,4] => [3,2,5,1,4] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,4,2,1,5] => [3,5,2,1,4] => [5]
=> []
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,4,2,5,1] => [3,5,2,4,1] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,4,5,2,1] => [3,5,4,2,1] => [5]
=> []
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,5,2,1,4] => [3,5,2,1,4] => [5]
=> []
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,5,2,4,1] => [3,5,2,4,1] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,5,4,2,1] => [3,5,4,2,1] => [5]
=> []
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[4,1,2,3,5] => [4,1,5,3,2] => [5]
=> []
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[4,1,2,5,3] => [4,1,5,3,2] => [5]
=> []
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[4,1,3,2,5] => [4,1,5,3,2] => [5]
=> []
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[4,1,3,5,2] => [4,1,5,3,2] => [5]
=> []
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
Description
The product of the parts of an integer partition.
Matching statistic: St000933
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00068: Permutations —Simion-Schmidt map⟶ Permutations
Mp00108: Permutations —cycle type⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000933: Integer partitions ⟶ ℤResult quality: 54% ●values known / values provided: 54%●distinct values known / distinct values provided: 67%
Mp00108: Permutations —cycle type⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000933: Integer partitions ⟶ ℤResult quality: 54% ●values known / values provided: 54%●distinct values known / distinct values provided: 67%
Values
[1,2] => [1,2] => [1,1]
=> [1]
=> ? ∊ {0,1}
[2,1] => [2,1] => [2]
=> []
=> ? ∊ {0,1}
[1,2,3] => [1,3,2] => [2,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1}
[1,3,2] => [1,3,2] => [2,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1}
[2,1,3] => [2,1,3] => [2,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1}
[2,3,1] => [2,3,1] => [3]
=> []
=> ? ∊ {0,1,1,1,1,1}
[3,1,2] => [3,1,2] => [3]
=> []
=> ? ∊ {0,1,1,1,1,1}
[3,2,1] => [3,2,1] => [2,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1}
[1,2,3,4] => [1,4,3,2] => [2,1,1]
=> [1,1]
=> 1
[1,2,4,3] => [1,4,3,2] => [2,1,1]
=> [1,1]
=> 1
[1,3,2,4] => [1,4,3,2] => [2,1,1]
=> [1,1]
=> 1
[1,3,4,2] => [1,4,3,2] => [2,1,1]
=> [1,1]
=> 1
[1,4,2,3] => [1,4,3,2] => [2,1,1]
=> [1,1]
=> 1
[1,4,3,2] => [1,4,3,2] => [2,1,1]
=> [1,1]
=> 1
[2,1,3,4] => [2,1,4,3] => [2,2]
=> [2]
=> 2
[2,1,4,3] => [2,1,4,3] => [2,2]
=> [2]
=> 2
[2,3,1,4] => [2,4,1,3] => [4]
=> []
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2}
[2,3,4,1] => [2,4,3,1] => [3,1]
=> [1]
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2}
[2,4,1,3] => [2,4,1,3] => [4]
=> []
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2}
[2,4,3,1] => [2,4,3,1] => [3,1]
=> [1]
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2}
[3,1,2,4] => [3,1,4,2] => [4]
=> []
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2}
[3,1,4,2] => [3,1,4,2] => [4]
=> []
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2}
[3,2,1,4] => [3,2,1,4] => [2,1,1]
=> [1,1]
=> 1
[3,2,4,1] => [3,2,4,1] => [3,1]
=> [1]
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2}
[3,4,1,2] => [3,4,1,2] => [2,2]
=> [2]
=> 2
[3,4,2,1] => [3,4,2,1] => [4]
=> []
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2}
[4,1,2,3] => [4,1,3,2] => [3,1]
=> [1]
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2}
[4,1,3,2] => [4,1,3,2] => [3,1]
=> [1]
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2}
[4,2,1,3] => [4,2,1,3] => [3,1]
=> [1]
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2}
[4,2,3,1] => [4,2,3,1] => [2,1,1]
=> [1,1]
=> 1
[4,3,1,2] => [4,3,1,2] => [4]
=> []
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2}
[4,3,2,1] => [4,3,2,1] => [2,2]
=> [2]
=> 2
[1,2,3,4,5] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,2,3,5,4] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,2,4,3,5] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,2,4,5,3] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,2,5,3,4] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,2,5,4,3] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,3,2,4,5] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,3,2,5,4] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,3,4,2,5] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,3,4,5,2] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,3,5,2,4] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,3,5,4,2] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,4,2,3,5] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,4,2,5,3] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,4,3,2,5] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,4,3,5,2] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,4,5,2,3] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,4,5,3,2] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,5,2,3,4] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,5,2,4,3] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,5,3,2,4] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,5,3,4,2] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,5,4,2,3] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[1,5,4,3,2] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 2
[2,1,3,4,5] => [2,1,5,4,3] => [2,2,1]
=> [2,1]
=> 2
[2,1,3,5,4] => [2,1,5,4,3] => [2,2,1]
=> [2,1]
=> 2
[2,1,4,3,5] => [2,1,5,4,3] => [2,2,1]
=> [2,1]
=> 2
[2,1,4,5,3] => [2,1,5,4,3] => [2,2,1]
=> [2,1]
=> 2
[2,1,5,3,4] => [2,1,5,4,3] => [2,2,1]
=> [2,1]
=> 2
[2,1,5,4,3] => [2,1,5,4,3] => [2,2,1]
=> [2,1]
=> 2
[2,3,1,4,5] => [2,5,1,4,3] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,3,1,5,4] => [2,5,1,4,3] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,3,4,1,5] => [2,5,4,1,3] => [5]
=> []
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,3,4,5,1] => [2,5,4,3,1] => [3,2]
=> [2]
=> 2
[2,3,5,1,4] => [2,5,4,1,3] => [5]
=> []
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,3,5,4,1] => [2,5,4,3,1] => [3,2]
=> [2]
=> 2
[2,4,1,3,5] => [2,5,1,4,3] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,4,1,5,3] => [2,5,1,4,3] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,4,3,1,5] => [2,5,4,1,3] => [5]
=> []
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,4,3,5,1] => [2,5,4,3,1] => [3,2]
=> [2]
=> 2
[2,4,5,1,3] => [2,5,4,1,3] => [5]
=> []
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,4,5,3,1] => [2,5,4,3,1] => [3,2]
=> [2]
=> 2
[2,5,1,3,4] => [2,5,1,4,3] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,5,1,4,3] => [2,5,1,4,3] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,5,3,1,4] => [2,5,4,1,3] => [5]
=> []
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,5,3,4,1] => [2,5,4,3,1] => [3,2]
=> [2]
=> 2
[2,5,4,1,3] => [2,5,4,1,3] => [5]
=> []
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,5,4,3,1] => [2,5,4,3,1] => [3,2]
=> [2]
=> 2
[3,1,2,4,5] => [3,1,5,4,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,1,2,5,4] => [3,1,5,4,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,1,4,2,5] => [3,1,5,4,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,1,4,5,2] => [3,1,5,4,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,1,5,2,4] => [3,1,5,4,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,1,5,4,2] => [3,1,5,4,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,2,1,4,5] => [3,2,1,5,4] => [2,2,1]
=> [2,1]
=> 2
[3,2,1,5,4] => [3,2,1,5,4] => [2,2,1]
=> [2,1]
=> 2
[3,2,4,1,5] => [3,2,5,1,4] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,2,5,1,4] => [3,2,5,1,4] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,4,2,1,5] => [3,5,2,1,4] => [5]
=> []
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,4,2,5,1] => [3,5,2,4,1] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,4,5,2,1] => [3,5,4,2,1] => [5]
=> []
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,5,2,1,4] => [3,5,2,1,4] => [5]
=> []
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,5,2,4,1] => [3,5,2,4,1] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,5,4,2,1] => [3,5,4,2,1] => [5]
=> []
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[4,1,2,3,5] => [4,1,5,3,2] => [5]
=> []
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[4,1,2,5,3] => [4,1,5,3,2] => [5]
=> []
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[4,1,3,2,5] => [4,1,5,3,2] => [5]
=> []
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[4,1,3,5,2] => [4,1,5,3,2] => [5]
=> []
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
Description
The number of multipartitions of sizes given by an integer partition.
This is, for $\lambda = (\lambda_1,\ldots,\lambda_n)$, this is the number of $n$-tuples $(\lambda^{(1)},\ldots,\lambda^{(n)})$ of partitions $\lambda^{(i)}$ such that $\lambda^{(i)} \vdash \lambda_i$.
Matching statistic: St000514
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00068: Permutations —Simion-Schmidt map⟶ Permutations
Mp00204: Permutations —LLPS⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000514: Integer partitions ⟶ ℤResult quality: 33% ●values known / values provided: 49%●distinct values known / distinct values provided: 33%
Mp00204: Permutations —LLPS⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000514: Integer partitions ⟶ ℤResult quality: 33% ●values known / values provided: 49%●distinct values known / distinct values provided: 33%
Values
[1,2] => [1,2] => [1,1]
=> [1]
=> ? ∊ {0,1}
[2,1] => [2,1] => [2]
=> []
=> ? ∊ {0,1}
[1,2,3] => [1,3,2] => [2,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1}
[1,3,2] => [1,3,2] => [2,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1}
[2,1,3] => [2,1,3] => [2,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1}
[2,3,1] => [2,3,1] => [2,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1}
[3,1,2] => [3,1,2] => [2,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1}
[3,2,1] => [3,2,1] => [3]
=> []
=> ? ∊ {0,1,1,1,1,1}
[1,2,3,4] => [1,4,3,2] => [3,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[1,2,4,3] => [1,4,3,2] => [3,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[1,3,2,4] => [1,4,3,2] => [3,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[1,3,4,2] => [1,4,3,2] => [3,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[1,4,2,3] => [1,4,3,2] => [3,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[1,4,3,2] => [1,4,3,2] => [3,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[2,1,3,4] => [2,1,4,3] => [2,2]
=> [2]
=> 2
[2,1,4,3] => [2,1,4,3] => [2,2]
=> [2]
=> 2
[2,3,1,4] => [2,4,1,3] => [2,1,1]
=> [1,1]
=> 2
[2,3,4,1] => [2,4,3,1] => [3,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[2,4,1,3] => [2,4,1,3] => [2,1,1]
=> [1,1]
=> 2
[2,4,3,1] => [2,4,3,1] => [3,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[3,1,2,4] => [3,1,4,2] => [2,2]
=> [2]
=> 2
[3,1,4,2] => [3,1,4,2] => [2,2]
=> [2]
=> 2
[3,2,1,4] => [3,2,1,4] => [3,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[3,2,4,1] => [3,2,4,1] => [3,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[3,4,1,2] => [3,4,1,2] => [2,1,1]
=> [1,1]
=> 2
[3,4,2,1] => [3,4,2,1] => [3,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[4,1,2,3] => [4,1,3,2] => [3,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[4,1,3,2] => [4,1,3,2] => [3,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[4,2,1,3] => [4,2,1,3] => [3,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[4,2,3,1] => [4,2,3,1] => [3,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[4,3,1,2] => [4,3,1,2] => [3,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[4,3,2,1] => [4,3,2,1] => [4]
=> []
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[1,2,3,4,5] => [1,5,4,3,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,2,3,5,4] => [1,5,4,3,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,2,4,3,5] => [1,5,4,3,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,2,4,5,3] => [1,5,4,3,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,2,5,3,4] => [1,5,4,3,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,2,5,4,3] => [1,5,4,3,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,3,2,4,5] => [1,5,4,3,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,3,2,5,4] => [1,5,4,3,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,3,4,2,5] => [1,5,4,3,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,3,4,5,2] => [1,5,4,3,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,3,5,2,4] => [1,5,4,3,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,3,5,4,2] => [1,5,4,3,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,4,2,3,5] => [1,5,4,3,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,4,2,5,3] => [1,5,4,3,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,4,3,2,5] => [1,5,4,3,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,4,3,5,2] => [1,5,4,3,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,4,5,2,3] => [1,5,4,3,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,4,5,3,2] => [1,5,4,3,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,5,2,3,4] => [1,5,4,3,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,5,2,4,3] => [1,5,4,3,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,5,3,2,4] => [1,5,4,3,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,5,3,4,2] => [1,5,4,3,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,5,4,2,3] => [1,5,4,3,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,5,4,3,2] => [1,5,4,3,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,1,3,4,5] => [2,1,5,4,3] => [3,2]
=> [2]
=> 2
[2,1,3,5,4] => [2,1,5,4,3] => [3,2]
=> [2]
=> 2
[2,1,4,3,5] => [2,1,5,4,3] => [3,2]
=> [2]
=> 2
[2,1,4,5,3] => [2,1,5,4,3] => [3,2]
=> [2]
=> 2
[2,1,5,3,4] => [2,1,5,4,3] => [3,2]
=> [2]
=> 2
[2,1,5,4,3] => [2,1,5,4,3] => [3,2]
=> [2]
=> 2
[2,3,1,4,5] => [2,5,1,4,3] => [3,1,1]
=> [1,1]
=> 2
[2,3,1,5,4] => [2,5,1,4,3] => [3,1,1]
=> [1,1]
=> 2
[2,3,4,1,5] => [2,5,4,1,3] => [3,1,1]
=> [1,1]
=> 2
[2,3,4,5,1] => [2,5,4,3,1] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,3,5,1,4] => [2,5,4,1,3] => [3,1,1]
=> [1,1]
=> 2
[2,4,1,3,5] => [2,5,1,4,3] => [3,1,1]
=> [1,1]
=> 2
[2,4,1,5,3] => [2,5,1,4,3] => [3,1,1]
=> [1,1]
=> 2
[2,4,3,1,5] => [2,5,4,1,3] => [3,1,1]
=> [1,1]
=> 2
[2,4,5,1,3] => [2,5,4,1,3] => [3,1,1]
=> [1,1]
=> 2
[2,5,1,3,4] => [2,5,1,4,3] => [3,1,1]
=> [1,1]
=> 2
[2,5,1,4,3] => [2,5,1,4,3] => [3,1,1]
=> [1,1]
=> 2
[2,5,3,1,4] => [2,5,4,1,3] => [3,1,1]
=> [1,1]
=> 2
[2,5,4,1,3] => [2,5,4,1,3] => [3,1,1]
=> [1,1]
=> 2
[3,1,2,4,5] => [3,1,5,4,2] => [3,2]
=> [2]
=> 2
[3,1,2,5,4] => [3,1,5,4,2] => [3,2]
=> [2]
=> 2
[3,1,4,2,5] => [3,1,5,4,2] => [3,2]
=> [2]
=> 2
[3,1,4,5,2] => [3,1,5,4,2] => [3,2]
=> [2]
=> 2
[3,1,5,2,4] => [3,1,5,4,2] => [3,2]
=> [2]
=> 2
[3,1,5,4,2] => [3,1,5,4,2] => [3,2]
=> [2]
=> 2
[3,2,1,4,5] => [3,2,1,5,4] => [3,2]
=> [2]
=> 2
[3,2,1,5,4] => [3,2,1,5,4] => [3,2]
=> [2]
=> 2
[3,2,4,1,5] => [3,2,5,1,4] => [3,1,1]
=> [1,1]
=> 2
[3,2,4,5,1] => [3,2,5,4,1] => [3,2]
=> [2]
=> 2
[3,2,5,1,4] => [3,2,5,1,4] => [3,1,1]
=> [1,1]
=> 2
[3,2,5,4,1] => [3,2,5,4,1] => [3,2]
=> [2]
=> 2
[3,4,1,2,5] => [3,5,1,4,2] => [3,1,1]
=> [1,1]
=> 2
[3,4,1,5,2] => [3,5,1,4,2] => [3,1,1]
=> [1,1]
=> 2
[3,4,2,1,5] => [3,5,2,1,4] => [3,1,1]
=> [1,1]
=> 2
[3,4,2,5,1] => [3,5,2,4,1] => [3,1,1]
=> [1,1]
=> 2
[3,4,5,1,2] => [3,5,4,1,2] => [3,1,1]
=> [1,1]
=> 2
[3,5,1,2,4] => [3,5,1,4,2] => [3,1,1]
=> [1,1]
=> 2
[3,5,1,4,2] => [3,5,1,4,2] => [3,1,1]
=> [1,1]
=> 2
[3,5,2,1,4] => [3,5,2,1,4] => [3,1,1]
=> [1,1]
=> 2
[3,5,2,4,1] => [3,5,2,4,1] => [3,1,1]
=> [1,1]
=> 2
[3,5,4,1,2] => [3,5,4,1,2] => [3,1,1]
=> [1,1]
=> 2
[4,1,2,3,5] => [4,1,5,3,2] => [3,2]
=> [2]
=> 2
[4,1,2,5,3] => [4,1,5,3,2] => [3,2]
=> [2]
=> 2
[4,1,3,2,5] => [4,1,5,3,2] => [3,2]
=> [2]
=> 2
Description
The number of invariant simple graphs when acting with a permutation of given cycle type.
Matching statistic: St000515
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00068: Permutations —Simion-Schmidt map⟶ Permutations
Mp00204: Permutations —LLPS⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000515: Integer partitions ⟶ ℤResult quality: 33% ●values known / values provided: 49%●distinct values known / distinct values provided: 33%
Mp00204: Permutations —LLPS⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000515: Integer partitions ⟶ ℤResult quality: 33% ●values known / values provided: 49%●distinct values known / distinct values provided: 33%
Values
[1,2] => [1,2] => [1,1]
=> [1]
=> ? ∊ {0,1}
[2,1] => [2,1] => [2]
=> []
=> ? ∊ {0,1}
[1,2,3] => [1,3,2] => [2,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1}
[1,3,2] => [1,3,2] => [2,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1}
[2,1,3] => [2,1,3] => [2,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1}
[2,3,1] => [2,3,1] => [2,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1}
[3,1,2] => [3,1,2] => [2,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1}
[3,2,1] => [3,2,1] => [3]
=> []
=> ? ∊ {0,1,1,1,1,1}
[1,2,3,4] => [1,4,3,2] => [3,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[1,2,4,3] => [1,4,3,2] => [3,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[1,3,2,4] => [1,4,3,2] => [3,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[1,3,4,2] => [1,4,3,2] => [3,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[1,4,2,3] => [1,4,3,2] => [3,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[1,4,3,2] => [1,4,3,2] => [3,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[2,1,3,4] => [2,1,4,3] => [2,2]
=> [2]
=> 2
[2,1,4,3] => [2,1,4,3] => [2,2]
=> [2]
=> 2
[2,3,1,4] => [2,4,1,3] => [2,1,1]
=> [1,1]
=> 2
[2,3,4,1] => [2,4,3,1] => [3,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[2,4,1,3] => [2,4,1,3] => [2,1,1]
=> [1,1]
=> 2
[2,4,3,1] => [2,4,3,1] => [3,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[3,1,2,4] => [3,1,4,2] => [2,2]
=> [2]
=> 2
[3,1,4,2] => [3,1,4,2] => [2,2]
=> [2]
=> 2
[3,2,1,4] => [3,2,1,4] => [3,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[3,2,4,1] => [3,2,4,1] => [3,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[3,4,1,2] => [3,4,1,2] => [2,1,1]
=> [1,1]
=> 2
[3,4,2,1] => [3,4,2,1] => [3,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[4,1,2,3] => [4,1,3,2] => [3,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[4,1,3,2] => [4,1,3,2] => [3,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[4,2,1,3] => [4,2,1,3] => [3,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[4,2,3,1] => [4,2,3,1] => [3,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[4,3,1,2] => [4,3,1,2] => [3,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[4,3,2,1] => [4,3,2,1] => [4]
=> []
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[1,2,3,4,5] => [1,5,4,3,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,2,3,5,4] => [1,5,4,3,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,2,4,3,5] => [1,5,4,3,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,2,4,5,3] => [1,5,4,3,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,2,5,3,4] => [1,5,4,3,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,2,5,4,3] => [1,5,4,3,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,3,2,4,5] => [1,5,4,3,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,3,2,5,4] => [1,5,4,3,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,3,4,2,5] => [1,5,4,3,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,3,4,5,2] => [1,5,4,3,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,3,5,2,4] => [1,5,4,3,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,3,5,4,2] => [1,5,4,3,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,4,2,3,5] => [1,5,4,3,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,4,2,5,3] => [1,5,4,3,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,4,3,2,5] => [1,5,4,3,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,4,3,5,2] => [1,5,4,3,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,4,5,2,3] => [1,5,4,3,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,4,5,3,2] => [1,5,4,3,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,5,2,3,4] => [1,5,4,3,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,5,2,4,3] => [1,5,4,3,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,5,3,2,4] => [1,5,4,3,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,5,3,4,2] => [1,5,4,3,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,5,4,2,3] => [1,5,4,3,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,5,4,3,2] => [1,5,4,3,2] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,1,3,4,5] => [2,1,5,4,3] => [3,2]
=> [2]
=> 2
[2,1,3,5,4] => [2,1,5,4,3] => [3,2]
=> [2]
=> 2
[2,1,4,3,5] => [2,1,5,4,3] => [3,2]
=> [2]
=> 2
[2,1,4,5,3] => [2,1,5,4,3] => [3,2]
=> [2]
=> 2
[2,1,5,3,4] => [2,1,5,4,3] => [3,2]
=> [2]
=> 2
[2,1,5,4,3] => [2,1,5,4,3] => [3,2]
=> [2]
=> 2
[2,3,1,4,5] => [2,5,1,4,3] => [3,1,1]
=> [1,1]
=> 2
[2,3,1,5,4] => [2,5,1,4,3] => [3,1,1]
=> [1,1]
=> 2
[2,3,4,1,5] => [2,5,4,1,3] => [3,1,1]
=> [1,1]
=> 2
[2,3,4,5,1] => [2,5,4,3,1] => [4,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,3,5,1,4] => [2,5,4,1,3] => [3,1,1]
=> [1,1]
=> 2
[2,4,1,3,5] => [2,5,1,4,3] => [3,1,1]
=> [1,1]
=> 2
[2,4,1,5,3] => [2,5,1,4,3] => [3,1,1]
=> [1,1]
=> 2
[2,4,3,1,5] => [2,5,4,1,3] => [3,1,1]
=> [1,1]
=> 2
[2,4,5,1,3] => [2,5,4,1,3] => [3,1,1]
=> [1,1]
=> 2
[2,5,1,3,4] => [2,5,1,4,3] => [3,1,1]
=> [1,1]
=> 2
[2,5,1,4,3] => [2,5,1,4,3] => [3,1,1]
=> [1,1]
=> 2
[2,5,3,1,4] => [2,5,4,1,3] => [3,1,1]
=> [1,1]
=> 2
[2,5,4,1,3] => [2,5,4,1,3] => [3,1,1]
=> [1,1]
=> 2
[3,1,2,4,5] => [3,1,5,4,2] => [3,2]
=> [2]
=> 2
[3,1,2,5,4] => [3,1,5,4,2] => [3,2]
=> [2]
=> 2
[3,1,4,2,5] => [3,1,5,4,2] => [3,2]
=> [2]
=> 2
[3,1,4,5,2] => [3,1,5,4,2] => [3,2]
=> [2]
=> 2
[3,1,5,2,4] => [3,1,5,4,2] => [3,2]
=> [2]
=> 2
[3,1,5,4,2] => [3,1,5,4,2] => [3,2]
=> [2]
=> 2
[3,2,1,4,5] => [3,2,1,5,4] => [3,2]
=> [2]
=> 2
[3,2,1,5,4] => [3,2,1,5,4] => [3,2]
=> [2]
=> 2
[3,2,4,1,5] => [3,2,5,1,4] => [3,1,1]
=> [1,1]
=> 2
[3,2,4,5,1] => [3,2,5,4,1] => [3,2]
=> [2]
=> 2
[3,2,5,1,4] => [3,2,5,1,4] => [3,1,1]
=> [1,1]
=> 2
[3,2,5,4,1] => [3,2,5,4,1] => [3,2]
=> [2]
=> 2
[3,4,1,2,5] => [3,5,1,4,2] => [3,1,1]
=> [1,1]
=> 2
[3,4,1,5,2] => [3,5,1,4,2] => [3,1,1]
=> [1,1]
=> 2
[3,4,2,1,5] => [3,5,2,1,4] => [3,1,1]
=> [1,1]
=> 2
[3,4,2,5,1] => [3,5,2,4,1] => [3,1,1]
=> [1,1]
=> 2
[3,4,5,1,2] => [3,5,4,1,2] => [3,1,1]
=> [1,1]
=> 2
[3,5,1,2,4] => [3,5,1,4,2] => [3,1,1]
=> [1,1]
=> 2
[3,5,1,4,2] => [3,5,1,4,2] => [3,1,1]
=> [1,1]
=> 2
[3,5,2,1,4] => [3,5,2,1,4] => [3,1,1]
=> [1,1]
=> 2
[3,5,2,4,1] => [3,5,2,4,1] => [3,1,1]
=> [1,1]
=> 2
[3,5,4,1,2] => [3,5,4,1,2] => [3,1,1]
=> [1,1]
=> 2
[4,1,2,3,5] => [4,1,5,3,2] => [3,2]
=> [2]
=> 2
[4,1,2,5,3] => [4,1,5,3,2] => [3,2]
=> [2]
=> 2
[4,1,3,2,5] => [4,1,5,3,2] => [3,2]
=> [2]
=> 2
Description
The number of invariant set partitions when acting with a permutation of given cycle type.
Matching statistic: St001568
(load all 3 compositions to match this statistic)
(load all 3 compositions to match this statistic)
Mp00252: Permutations —restriction⟶ Permutations
Mp00204: Permutations —LLPS⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001568: Integer partitions ⟶ ℤResult quality: 49% ●values known / values provided: 49%●distinct values known / distinct values provided: 67%
Mp00204: Permutations —LLPS⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001568: Integer partitions ⟶ ℤResult quality: 49% ●values known / values provided: 49%●distinct values known / distinct values provided: 67%
Values
[1,2] => [1] => [1]
=> []
=> ? ∊ {0,1}
[2,1] => [1] => [1]
=> []
=> ? ∊ {0,1}
[1,2,3] => [1,2] => [1,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1}
[1,3,2] => [1,2] => [1,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1}
[2,1,3] => [2,1] => [2]
=> []
=> ? ∊ {0,1,1,1,1,1}
[2,3,1] => [2,1] => [2]
=> []
=> ? ∊ {0,1,1,1,1,1}
[3,1,2] => [1,2] => [1,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1}
[3,2,1] => [2,1] => [2]
=> []
=> ? ∊ {0,1,1,1,1,1}
[1,2,3,4] => [1,2,3] => [1,1,1]
=> [1,1]
=> 2
[1,2,4,3] => [1,2,3] => [1,1,1]
=> [1,1]
=> 2
[1,3,2,4] => [1,3,2] => [2,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2}
[1,3,4,2] => [1,3,2] => [2,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2}
[1,4,2,3] => [1,2,3] => [1,1,1]
=> [1,1]
=> 2
[1,4,3,2] => [1,3,2] => [2,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2}
[2,1,3,4] => [2,1,3] => [2,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2}
[2,1,4,3] => [2,1,3] => [2,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2}
[2,3,1,4] => [2,3,1] => [2,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2}
[2,3,4,1] => [2,3,1] => [2,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2}
[2,4,1,3] => [2,1,3] => [2,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2}
[2,4,3,1] => [2,3,1] => [2,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2}
[3,1,2,4] => [3,1,2] => [2,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2}
[3,1,4,2] => [3,1,2] => [2,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2}
[3,2,1,4] => [3,2,1] => [3]
=> []
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2}
[3,2,4,1] => [3,2,1] => [3]
=> []
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2}
[3,4,1,2] => [3,1,2] => [2,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2}
[3,4,2,1] => [3,2,1] => [3]
=> []
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2}
[4,1,2,3] => [1,2,3] => [1,1,1]
=> [1,1]
=> 2
[4,1,3,2] => [1,3,2] => [2,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2}
[4,2,1,3] => [2,1,3] => [2,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2}
[4,2,3,1] => [2,3,1] => [2,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2}
[4,3,1,2] => [3,1,2] => [2,1]
=> [1]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2}
[4,3,2,1] => [3,2,1] => [3]
=> []
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2}
[1,2,3,4,5] => [1,2,3,4] => [1,1,1,1]
=> [1,1,1]
=> 2
[1,2,3,5,4] => [1,2,3,4] => [1,1,1,1]
=> [1,1,1]
=> 2
[1,2,4,3,5] => [1,2,4,3] => [2,1,1]
=> [1,1]
=> 2
[1,2,4,5,3] => [1,2,4,3] => [2,1,1]
=> [1,1]
=> 2
[1,2,5,3,4] => [1,2,3,4] => [1,1,1,1]
=> [1,1,1]
=> 2
[1,2,5,4,3] => [1,2,4,3] => [2,1,1]
=> [1,1]
=> 2
[1,3,2,4,5] => [1,3,2,4] => [2,1,1]
=> [1,1]
=> 2
[1,3,2,5,4] => [1,3,2,4] => [2,1,1]
=> [1,1]
=> 2
[1,3,4,2,5] => [1,3,4,2] => [2,1,1]
=> [1,1]
=> 2
[1,3,4,5,2] => [1,3,4,2] => [2,1,1]
=> [1,1]
=> 2
[1,3,5,2,4] => [1,3,2,4] => [2,1,1]
=> [1,1]
=> 2
[1,3,5,4,2] => [1,3,4,2] => [2,1,1]
=> [1,1]
=> 2
[1,4,2,3,5] => [1,4,2,3] => [2,1,1]
=> [1,1]
=> 2
[1,4,2,5,3] => [1,4,2,3] => [2,1,1]
=> [1,1]
=> 2
[1,4,3,2,5] => [1,4,3,2] => [3,1]
=> [1]
=> ? ∊ {0,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,4,3,5,2] => [1,4,3,2] => [3,1]
=> [1]
=> ? ∊ {0,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,4,5,2,3] => [1,4,2,3] => [2,1,1]
=> [1,1]
=> 2
[1,4,5,3,2] => [1,4,3,2] => [3,1]
=> [1]
=> ? ∊ {0,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,5,2,3,4] => [1,2,3,4] => [1,1,1,1]
=> [1,1,1]
=> 2
[1,5,2,4,3] => [1,2,4,3] => [2,1,1]
=> [1,1]
=> 2
[1,5,3,2,4] => [1,3,2,4] => [2,1,1]
=> [1,1]
=> 2
[1,5,3,4,2] => [1,3,4,2] => [2,1,1]
=> [1,1]
=> 2
[1,5,4,2,3] => [1,4,2,3] => [2,1,1]
=> [1,1]
=> 2
[1,5,4,3,2] => [1,4,3,2] => [3,1]
=> [1]
=> ? ∊ {0,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,1,3,4,5] => [2,1,3,4] => [2,1,1]
=> [1,1]
=> 2
[2,1,3,5,4] => [2,1,3,4] => [2,1,1]
=> [1,1]
=> 2
[2,1,4,3,5] => [2,1,4,3] => [2,2]
=> [2]
=> 1
[2,1,4,5,3] => [2,1,4,3] => [2,2]
=> [2]
=> 1
[2,1,5,3,4] => [2,1,3,4] => [2,1,1]
=> [1,1]
=> 2
[2,1,5,4,3] => [2,1,4,3] => [2,2]
=> [2]
=> 1
[2,3,1,4,5] => [2,3,1,4] => [2,1,1]
=> [1,1]
=> 2
[2,3,1,5,4] => [2,3,1,4] => [2,1,1]
=> [1,1]
=> 2
[2,3,4,1,5] => [2,3,4,1] => [2,1,1]
=> [1,1]
=> 2
[2,3,4,5,1] => [2,3,4,1] => [2,1,1]
=> [1,1]
=> 2
[2,3,5,1,4] => [2,3,1,4] => [2,1,1]
=> [1,1]
=> 2
[2,3,5,4,1] => [2,3,4,1] => [2,1,1]
=> [1,1]
=> 2
[2,4,1,3,5] => [2,4,1,3] => [2,1,1]
=> [1,1]
=> 2
[2,4,1,5,3] => [2,4,1,3] => [2,1,1]
=> [1,1]
=> 2
[2,4,3,1,5] => [2,4,3,1] => [3,1]
=> [1]
=> ? ∊ {0,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,4,3,5,1] => [2,4,3,1] => [3,1]
=> [1]
=> ? ∊ {0,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,4,5,1,3] => [2,4,1,3] => [2,1,1]
=> [1,1]
=> 2
[2,4,5,3,1] => [2,4,3,1] => [3,1]
=> [1]
=> ? ∊ {0,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,5,1,3,4] => [2,1,3,4] => [2,1,1]
=> [1,1]
=> 2
[2,5,1,4,3] => [2,1,4,3] => [2,2]
=> [2]
=> 1
[2,5,3,1,4] => [2,3,1,4] => [2,1,1]
=> [1,1]
=> 2
[2,5,3,4,1] => [2,3,4,1] => [2,1,1]
=> [1,1]
=> 2
[2,5,4,1,3] => [2,4,1,3] => [2,1,1]
=> [1,1]
=> 2
[2,5,4,3,1] => [2,4,3,1] => [3,1]
=> [1]
=> ? ∊ {0,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,1,2,4,5] => [3,1,2,4] => [2,1,1]
=> [1,1]
=> 2
[3,1,2,5,4] => [3,1,2,4] => [2,1,1]
=> [1,1]
=> 2
[3,1,4,2,5] => [3,1,4,2] => [2,2]
=> [2]
=> 1
[3,1,4,5,2] => [3,1,4,2] => [2,2]
=> [2]
=> 1
[3,1,5,2,4] => [3,1,2,4] => [2,1,1]
=> [1,1]
=> 2
[3,1,5,4,2] => [3,1,4,2] => [2,2]
=> [2]
=> 1
[3,2,1,4,5] => [3,2,1,4] => [3,1]
=> [1]
=> ? ∊ {0,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,2,1,5,4] => [3,2,1,4] => [3,1]
=> [1]
=> ? ∊ {0,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,2,4,1,5] => [3,2,4,1] => [3,1]
=> [1]
=> ? ∊ {0,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,2,4,5,1] => [3,2,4,1] => [3,1]
=> [1]
=> ? ∊ {0,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,2,5,1,4] => [3,2,1,4] => [3,1]
=> [1]
=> ? ∊ {0,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,2,5,4,1] => [3,2,4,1] => [3,1]
=> [1]
=> ? ∊ {0,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,4,2,1,5] => [3,4,2,1] => [3,1]
=> [1]
=> ? ∊ {0,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,4,2,5,1] => [3,4,2,1] => [3,1]
=> [1]
=> ? ∊ {0,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,4,5,2,1] => [3,4,2,1] => [3,1]
=> [1]
=> ? ∊ {0,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,5,2,1,4] => [3,2,1,4] => [3,1]
=> [1]
=> ? ∊ {0,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,5,2,4,1] => [3,2,4,1] => [3,1]
=> [1]
=> ? ∊ {0,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[3,5,4,2,1] => [3,4,2,1] => [3,1]
=> [1]
=> ? ∊ {0,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[4,1,3,2,5] => [4,1,3,2] => [3,1]
=> [1]
=> ? ∊ {0,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[4,1,3,5,2] => [4,1,3,2] => [3,1]
=> [1]
=> ? ∊ {0,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
Description
The smallest positive integer that does not appear twice in the partition.
Matching statistic: St001198
(load all 3 compositions to match this statistic)
(load all 3 compositions to match this statistic)
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00103: Dyck paths —peeling map⟶ Dyck paths
Mp00030: Dyck paths —zeta map⟶ Dyck paths
St001198: Dyck paths ⟶ ℤResult quality: 33% ●values known / values provided: 47%●distinct values known / distinct values provided: 33%
Mp00103: Dyck paths —peeling map⟶ Dyck paths
Mp00030: Dyck paths —zeta map⟶ Dyck paths
St001198: Dyck paths ⟶ ℤResult quality: 33% ●values known / values provided: 47%●distinct values known / distinct values provided: 33%
Values
[1,2] => [1,0,1,0]
=> [1,0,1,0]
=> [1,1,0,0]
=> ? ∊ {0,1}
[2,1] => [1,1,0,0]
=> [1,0,1,0]
=> [1,1,0,0]
=> ? ∊ {0,1}
[1,2,3] => [1,0,1,0,1,0]
=> [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> ? ∊ {0,1,1,1,1,1}
[1,3,2] => [1,0,1,1,0,0]
=> [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> ? ∊ {0,1,1,1,1,1}
[2,1,3] => [1,1,0,0,1,0]
=> [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> ? ∊ {0,1,1,1,1,1}
[2,3,1] => [1,1,0,1,0,0]
=> [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> ? ∊ {0,1,1,1,1,1}
[3,1,2] => [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> ? ∊ {0,1,1,1,1,1}
[3,2,1] => [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> ? ∊ {0,1,1,1,1,1}
[1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2}
[1,2,4,3] => [1,0,1,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2}
[1,3,2,4] => [1,0,1,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2}
[1,3,4,2] => [1,0,1,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2}
[1,4,2,3] => [1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2}
[1,4,3,2] => [1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2}
[2,1,3,4] => [1,1,0,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2}
[2,1,4,3] => [1,1,0,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2}
[2,3,1,4] => [1,1,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2}
[2,3,4,1] => [1,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2}
[2,4,1,3] => [1,1,0,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2}
[2,4,3,1] => [1,1,0,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2}
[3,1,2,4] => [1,1,1,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2}
[3,1,4,2] => [1,1,1,0,0,1,0,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2}
[3,2,1,4] => [1,1,1,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2}
[3,2,4,1] => [1,1,1,0,0,1,0,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2}
[3,4,1,2] => [1,1,1,0,1,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2}
[3,4,2,1] => [1,1,1,0,1,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2}
[4,1,2,3] => [1,1,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,0,0,0]
=> 2
[4,1,3,2] => [1,1,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,0,0,0]
=> 2
[4,2,1,3] => [1,1,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,0,0,0]
=> 2
[4,2,3,1] => [1,1,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,0,0,0]
=> 2
[4,3,1,2] => [1,1,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,0,0,0]
=> 2
[4,3,2,1] => [1,1,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,0,0,0]
=> 2
[1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,2,5,3,4] => [1,0,1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,2,5,4,3] => [1,0,1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,3,4,2,5] => [1,0,1,1,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,3,5,2,4] => [1,0,1,1,0,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,3,5,4,2] => [1,0,1,1,0,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,4,2,5,3] => [1,0,1,1,1,0,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,4,3,2,5] => [1,0,1,1,1,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,4,3,5,2] => [1,0,1,1,1,0,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,4,5,2,3] => [1,0,1,1,1,0,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,4,5,3,2] => [1,0,1,1,1,0,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> 2
[1,5,2,4,3] => [1,0,1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> 2
[1,5,3,2,4] => [1,0,1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> 2
[1,5,3,4,2] => [1,0,1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> 2
[1,5,4,2,3] => [1,0,1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> 2
[1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> 2
[2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,1,3,5,4] => [1,1,0,0,1,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,1,4,5,3] => [1,1,0,0,1,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,1,5,3,4] => [1,1,0,0,1,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,1,5,4,3] => [1,1,0,0,1,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,5,1,3,4] => [1,1,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> 2
[2,5,1,4,3] => [1,1,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> 2
[2,5,3,1,4] => [1,1,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> 2
[2,5,3,4,1] => [1,1,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> 2
[2,5,4,1,3] => [1,1,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> 2
[2,5,4,3,1] => [1,1,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> 2
[3,5,1,2,4] => [1,1,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> 2
[3,5,1,4,2] => [1,1,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> 2
[3,5,2,1,4] => [1,1,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> 2
[3,5,2,4,1] => [1,1,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> 2
[3,5,4,1,2] => [1,1,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> 2
[3,5,4,2,1] => [1,1,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> 2
[4,1,2,3,5] => [1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> 2
[4,1,2,5,3] => [1,1,1,1,0,0,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> 2
[4,1,3,2,5] => [1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> 2
[4,1,3,5,2] => [1,1,1,1,0,0,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> 2
[4,1,5,2,3] => [1,1,1,1,0,0,1,0,0,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> 2
[4,1,5,3,2] => [1,1,1,1,0,0,1,0,0,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> 2
[4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> 2
[4,2,1,5,3] => [1,1,1,1,0,0,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> 2
[4,2,3,1,5] => [1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> 2
[4,2,3,5,1] => [1,1,1,1,0,0,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> 2
[4,2,5,1,3] => [1,1,1,1,0,0,1,0,0,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> 2
[4,2,5,3,1] => [1,1,1,1,0,0,1,0,0,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> 2
[4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> 2
[4,3,1,5,2] => [1,1,1,1,0,0,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> 2
[4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> 2
[4,3,2,5,1] => [1,1,1,1,0,0,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> 2
[4,3,5,1,2] => [1,1,1,1,0,0,1,0,0,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> 2
[4,3,5,2,1] => [1,1,1,1,0,0,1,0,0,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> 2
[4,5,1,2,3] => [1,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,0,1,0,0,1,0]
=> [1,1,1,0,0,1,1,0,0,0]
=> 2
[4,5,1,3,2] => [1,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,0,1,0,0,1,0]
=> [1,1,1,0,0,1,1,0,0,0]
=> 2
[4,5,2,1,3] => [1,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,0,1,0,0,1,0]
=> [1,1,1,0,0,1,1,0,0,0]
=> 2
[4,5,2,3,1] => [1,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,0,1,0,0,1,0]
=> [1,1,1,0,0,1,1,0,0,0]
=> 2
[4,5,3,1,2] => [1,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,0,1,0,0,1,0]
=> [1,1,1,0,0,1,1,0,0,0]
=> 2
[4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,0,1,0,0,1,0]
=> [1,1,1,0,0,1,1,0,0,0]
=> 2
[5,1,2,3,4] => [1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,1,1,0,0,0,1,0]
=> [1,0,1,1,0,1,1,0,0,0]
=> 2
[5,1,2,4,3] => [1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,1,1,0,0,0,1,0]
=> [1,0,1,1,0,1,1,0,0,0]
=> 2
Description
The number of simple modules in the algebra $eAe$ with projective dimension at most 1 in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$.
The following 28 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St001206The maximal dimension of an indecomposable projective $eAe$-module (that is the height of the corresponding Dyck path) of the corresponding Nakayama algebra with minimal faithful projective-injective module $eA$. St000454The largest eigenvalue of a graph if it is integral. St001896The number of right descents of a signed permutations. St001630The global dimension of the incidence algebra of the lattice over the rational numbers. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St000455The second largest eigenvalue of a graph if it is integral. St000527The width of the poset. St000845The maximal number of elements covered by an element in a poset. St000846The maximal number of elements covering an element of a poset. St001632The number of indecomposable injective modules $I$ with $dim Ext^1(I,A)=1$ for the incidence algebra A of a poset. St000770The major index of an integer partition when read from bottom to top. St000815The number of semistandard Young tableaux of partition weight of given shape. St000937The number of positive values of the symmetric group character corresponding to the partition. St001605The number of colourings of a cycle such that the multiplicities of colours are given by a partition. St000633The size of the automorphism group of a poset. St000640The rank of the largest boolean interval in a poset. St000910The number of maximal chains of minimal length in a poset. St001105The number of greedy linear extensions of a poset. St001106The number of supergreedy linear extensions of a poset. St001085The number of occurrences of the vincular pattern |21-3 in a permutation. St000862The number of parts of the shifted shape of a permutation. St001624The breadth of a lattice. St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset. St000259The diameter of a connected graph. St000771The largest multiplicity of a distance Laplacian eigenvalue in a connected graph. St000772The multiplicity of the largest distance Laplacian eigenvalue in a connected graph. St001878The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L. St001877Number of indecomposable injective modules with projective dimension 2.
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