- FindStat

Your data matches 61 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)

Matching statistic: St001469

Mapping

St001469: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

[1] => 0
[1,2] => 0
[2,1] => 0
[1,2,3] => 0
[1,3,2] => 1
[2,1,3] => 1
[2,3,1] => 1
[3,1,2] => 1
[3,2,1] => 0
[1,2,3,4] => 0
[1,2,4,3] => 1
[1,3,2,4] => 1
[1,3,4,2] => 1
[1,4,2,3] => 1
[1,4,3,2] => 1
[2,1,3,4] => 1
[2,1,4,3] => 1
[2,3,1,4] => 1
[2,3,4,1] => 1
[2,4,1,3] => 1
[2,4,3,1] => 1
[3,1,2,4] => 1
[3,1,4,2] => 1
[3,2,1,4] => 1
[3,2,4,1] => 1
[3,4,1,2] => 1
[3,4,2,1] => 1
[4,1,2,3] => 1
[4,1,3,2] => 1
[4,2,1,3] => 1
[4,2,3,1] => 1
[4,3,1,2] => 1
[4,3,2,1] => 0
[1,2,3,4,5] => 0
[1,2,3,5,4] => 1
[1,2,4,3,5] => 1
[1,2,4,5,3] => 1
[1,2,5,3,4] => 1
[1,2,5,4,3] => 1
[1,3,2,4,5] => 1
[1,3,2,5,4] => 1
[1,3,4,2,5] => 1
[1,3,4,5,2] => 1
[1,3,5,2,4] => 2
[1,3,5,4,2] => 2
[1,4,2,3,5] => 1
[1,4,2,5,3] => 1
[1,4,3,2,5] => 1
[1,4,3,5,2] => 1
[1,4,5,2,3] => 1

Description

The holeyness of a permutation. For

$S\subset [n]:=\{1,2,\dots,n\}$ let

$\delta(S)$ be the number of elements

$m\in S$ such that

$m+1\notin S$ . For a permutation

$\pi$ of

$[n]$ the holeyness of

$\pi$ is

$\max_{S\subset [n]} (\delta(\pi(S))-\delta(S)).$

Matching statistic: St000260
(load all 14 compositions to match this statistic)

Mapping

Mp00068: Permutations —Simion-Schmidt map⟶ Permutations
Mp00252: Permutations —restriction⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000260: Graphs ⟶ ℤResult quality: 66% ●values known / values provided: 66%●distinct values known / distinct values provided: 100%

Values

[1] => [1] => [] => ([],0)
 => ? = 0
[1,2] => [1,2] => [1] => ([],1)
 => 0
[2,1] => [2,1] => [1] => ([],1)
 => 0
[1,2,3] => [1,3,2] => [1,2] => ([],2)
 => ? ∊ {0,0,1}
[1,3,2] => [1,3,2] => [1,2] => ([],2)
 => ? ∊ {0,0,1}
[2,1,3] => [2,1,3] => [2,1] => ([(0,1)],2)
 => 1
[2,3,1] => [2,3,1] => [2,1] => ([(0,1)],2)
 => 1
[3,1,2] => [3,1,2] => [1,2] => ([],2)
 => ? ∊ {0,0,1}
[3,2,1] => [3,2,1] => [2,1] => ([(0,1)],2)
 => 1
[1,2,3,4] => [1,4,3,2] => [1,3,2] => ([(1,2)],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1}
[1,2,4,3] => [1,4,3,2] => [1,3,2] => ([(1,2)],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1}
[1,3,2,4] => [1,4,3,2] => [1,3,2] => ([(1,2)],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1}
[1,3,4,2] => [1,4,3,2] => [1,3,2] => ([(1,2)],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1}
[1,4,2,3] => [1,4,3,2] => [1,3,2] => ([(1,2)],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1}
[1,4,3,2] => [1,4,3,2] => [1,3,2] => ([(1,2)],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1}
[2,1,3,4] => [2,1,4,3] => [2,1,3] => ([(1,2)],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1}
[2,1,4,3] => [2,1,4,3] => [2,1,3] => ([(1,2)],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1}
[2,3,1,4] => [2,4,1,3] => [2,1,3] => ([(1,2)],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1}
[2,3,4,1] => [2,4,3,1] => [2,3,1] => ([(0,2),(1,2)],3)
 => 1
[2,4,1,3] => [2,4,1,3] => [2,1,3] => ([(1,2)],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1}
[2,4,3,1] => [2,4,3,1] => [2,3,1] => ([(0,2),(1,2)],3)
 => 1
[3,1,2,4] => [3,1,4,2] => [3,1,2] => ([(0,2),(1,2)],3)
 => 1
[3,1,4,2] => [3,1,4,2] => [3,1,2] => ([(0,2),(1,2)],3)
 => 1
[3,2,1,4] => [3,2,1,4] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
 => 1
[3,2,4,1] => [3,2,4,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
 => 1
[3,4,1,2] => [3,4,1,2] => [3,1,2] => ([(0,2),(1,2)],3)
 => 1
[3,4,2,1] => [3,4,2,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
 => 1
[4,1,2,3] => [4,1,3,2] => [1,3,2] => ([(1,2)],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1}
[4,1,3,2] => [4,1,3,2] => [1,3,2] => ([(1,2)],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1}
[4,2,1,3] => [4,2,1,3] => [2,1,3] => ([(1,2)],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1}
[4,2,3,1] => [4,2,3,1] => [2,3,1] => ([(0,2),(1,2)],3)
 => 1
[4,3,1,2] => [4,3,1,2] => [3,1,2] => ([(0,2),(1,2)],3)
 => 1
[4,3,2,1] => [4,3,2,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
 => 1
[1,2,3,4,5] => [1,5,4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,2,3,5,4] => [1,5,4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,2,4,3,5] => [1,5,4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,2,4,5,3] => [1,5,4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,2,5,3,4] => [1,5,4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,2,5,4,3] => [1,5,4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,3,2,4,5] => [1,5,4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,3,2,5,4] => [1,5,4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,3,4,2,5] => [1,5,4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,3,4,5,2] => [1,5,4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,3,5,2,4] => [1,5,4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,3,5,4,2] => [1,5,4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,4,2,3,5] => [1,5,4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,4,2,5,3] => [1,5,4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,4,3,2,5] => [1,5,4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,4,3,5,2] => [1,5,4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,4,5,2,3] => [1,5,4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,4,5,3,2] => [1,5,4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,5,2,3,4] => [1,5,4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,5,2,4,3] => [1,5,4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,5,3,2,4] => [1,5,4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,5,3,4,2] => [1,5,4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,5,4,2,3] => [1,5,4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,5,4,3,2] => [1,5,4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,1,3,4,5] => [2,1,5,4,3] => [2,1,4,3] => ([(0,3),(1,2)],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,1,3,5,4] => [2,1,5,4,3] => [2,1,4,3] => ([(0,3),(1,2)],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,1,4,3,5] => [2,1,5,4,3] => [2,1,4,3] => ([(0,3),(1,2)],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,1,4,5,3] => [2,1,5,4,3] => [2,1,4,3] => ([(0,3),(1,2)],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,1,5,3,4] => [2,1,5,4,3] => [2,1,4,3] => ([(0,3),(1,2)],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,1,5,4,3] => [2,1,5,4,3] => [2,1,4,3] => ([(0,3),(1,2)],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,3,1,4,5] => [2,5,1,4,3] => [2,1,4,3] => ([(0,3),(1,2)],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,3,1,5,4] => [2,5,1,4,3] => [2,1,4,3] => ([(0,3),(1,2)],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,3,4,1,5] => [2,5,4,1,3] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
 => 2
[2,3,4,5,1] => [2,5,4,3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
[2,3,5,1,4] => [2,5,4,1,3] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
 => 2
[2,3,5,4,1] => [2,5,4,3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
[2,4,1,3,5] => [2,5,1,4,3] => [2,1,4,3] => ([(0,3),(1,2)],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,4,3,1,5] => [2,5,4,1,3] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
 => 2
[2,4,3,5,1] => [2,5,4,3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
[2,4,5,1,3] => [2,5,4,1,3] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
 => 2
[2,4,5,3,1] => [2,5,4,3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
[2,5,3,1,4] => [2,5,4,1,3] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
 => 2
[2,5,3,4,1] => [2,5,4,3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
[2,5,4,1,3] => [2,5,4,1,3] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
 => 2
[2,5,4,3,1] => [2,5,4,3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
[3,1,2,4,5] => [3,1,5,4,2] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
 => 2
[3,1,2,5,4] => [3,1,5,4,2] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
 => 2
[3,1,4,2,5] => [3,1,5,4,2] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
 => 2
[3,1,4,5,2] => [3,1,5,4,2] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
 => 2
[3,1,5,2,4] => [3,1,5,4,2] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
 => 2
[3,1,5,4,2] => [3,1,5,4,2] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
 => 2
[3,2,4,5,1] => [3,2,5,4,1] => [3,2,4,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
[3,2,5,4,1] => [3,2,5,4,1] => [3,2,4,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
[3,4,1,2,5] => [3,5,1,4,2] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
 => 2
[3,4,1,5,2] => [3,5,1,4,2] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
 => 2
[3,4,2,5,1] => [3,5,2,4,1] => [3,2,4,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
[3,4,5,1,2] => [3,5,4,1,2] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2
[3,4,5,2,1] => [3,5,4,2,1] => [3,4,2,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
[3,5,1,2,4] => [3,5,1,4,2] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
 => 2
[3,5,1,4,2] => [3,5,1,4,2] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
 => 2
[3,5,2,4,1] => [3,5,2,4,1] => [3,2,4,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
[3,5,4,1,2] => [3,5,4,1,2] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2
[3,5,4,2,1] => [3,5,4,2,1] => [3,4,2,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
[4,1,2,3,5] => [4,1,5,3,2] => [4,1,3,2] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
[4,1,2,5,3] => [4,1,5,3,2] => [4,1,3,2] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
[4,1,3,2,5] => [4,1,5,3,2] => [4,1,3,2] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
[4,1,3,5,2] => [4,1,5,3,2] => [4,1,3,2] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1

Description

The radius of a connected graph. This is the minimum eccentricity of any vertex.

Matching statistic: St000668
(load all 5 compositions to match this statistic)

Mapping

Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000668: Integer partitions ⟶ ℤResult quality: 62% ●values known / values provided: 62%●distinct values known / distinct values provided: 67%

Values

[1] => [1] => [1]
 => []
 => ? = 0
[1,2] => [1,2] => [2]
 => []
 => ? ∊ {0,0}
[2,1] => [1,2] => [2]
 => []
 => ? ∊ {0,0}
[1,2,3] => [1,2,3] => [3]
 => []
 => ? ∊ {0,0,1,1,1,1}
[1,3,2] => [1,2,3] => [3]
 => []
 => ? ∊ {0,0,1,1,1,1}
[2,1,3] => [1,2,3] => [3]
 => []
 => ? ∊ {0,0,1,1,1,1}
[2,3,1] => [1,2,3] => [3]
 => []
 => ? ∊ {0,0,1,1,1,1}
[3,1,2] => [1,3,2] => [2,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1}
[3,2,1] => [1,3,2] => [2,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1}
[1,2,3,4] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[1,2,4,3] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[1,3,2,4] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[1,3,4,2] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[1,4,2,3] => [1,2,4,3] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[1,4,3,2] => [1,2,4,3] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[2,1,3,4] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[2,1,4,3] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[2,3,1,4] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[2,3,4,1] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[2,4,1,3] => [1,2,4,3] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[2,4,3,1] => [1,2,4,3] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[3,1,2,4] => [1,3,2,4] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[3,1,4,2] => [1,3,4,2] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[3,2,1,4] => [1,3,2,4] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[3,2,4,1] => [1,3,4,2] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[3,4,1,2] => [1,3,2,4] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[3,4,2,1] => [1,3,2,4] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[4,1,2,3] => [1,4,3,2] => [2,1,1]
 => [1,1]
 => 1
[4,1,3,2] => [1,4,2,3] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[4,2,1,3] => [1,4,3,2] => [2,1,1]
 => [1,1]
 => 1
[4,2,3,1] => [1,4,2,3] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[4,3,1,2] => [1,4,2,3] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[4,3,2,1] => [1,4,2,3] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[1,2,3,4,5] => [1,2,3,4,5] => [5]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,2,3,5,4] => [1,2,3,4,5] => [5]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,2,4,3,5] => [1,2,3,4,5] => [5]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,2,4,5,3] => [1,2,3,4,5] => [5]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,2,5,3,4] => [1,2,3,5,4] => [4,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,2,5,4,3] => [1,2,3,5,4] => [4,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,3,2,4,5] => [1,2,3,4,5] => [5]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,3,2,5,4] => [1,2,3,4,5] => [5]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,3,4,2,5] => [1,2,3,4,5] => [5]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,3,4,5,2] => [1,2,3,4,5] => [5]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,3,5,2,4] => [1,2,3,5,4] => [4,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,3,5,4,2] => [1,2,3,5,4] => [4,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,4,2,3,5] => [1,2,4,3,5] => [4,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,4,2,5,3] => [1,2,4,5,3] => [4,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,4,3,2,5] => [1,2,4,3,5] => [4,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,4,3,5,2] => [1,2,4,5,3] => [4,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,4,5,2,3] => [1,2,4,3,5] => [4,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,4,5,3,2] => [1,2,4,3,5] => [4,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,5,2,3,4] => [1,2,5,4,3] => [3,1,1]
 => [1,1]
 => 1
[1,5,2,4,3] => [1,2,5,3,4] => [4,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,5,3,2,4] => [1,2,5,4,3] => [3,1,1]
 => [1,1]
 => 1
[2,5,1,3,4] => [1,2,5,4,3] => [3,1,1]
 => [1,1]
 => 1
[2,5,3,1,4] => [1,2,5,4,3] => [3,1,1]
 => [1,1]
 => 1
[3,1,5,2,4] => [1,3,5,4,2] => [3,1,1]
 => [1,1]
 => 1
[3,1,5,4,2] => [1,3,5,2,4] => [3,2]
 => [2]
 => 2
[3,2,5,1,4] => [1,3,5,4,2] => [3,1,1]
 => [1,1]
 => 1
[3,2,5,4,1] => [1,3,5,2,4] => [3,2]
 => [2]
 => 2
[3,4,5,1,2] => [1,3,5,2,4] => [3,2]
 => [2]
 => 2
[3,4,5,2,1] => [1,3,5,2,4] => [3,2]
 => [2]
 => 2
[3,5,1,2,4] => [1,3,2,5,4] => [3,2]
 => [2]
 => 2
[3,5,1,4,2] => [1,3,2,5,4] => [3,2]
 => [2]
 => 2
[3,5,2,1,4] => [1,3,2,5,4] => [3,2]
 => [2]
 => 2
[3,5,2,4,1] => [1,3,2,5,4] => [3,2]
 => [2]
 => 2
[4,1,2,3,5] => [1,4,3,2,5] => [3,1,1]
 => [1,1]
 => 1
[4,1,2,5,3] => [1,4,5,3,2] => [3,1,1]
 => [1,1]
 => 1
[4,1,3,5,2] => [1,4,5,2,3] => [3,2]
 => [2]
 => 2
[4,1,5,3,2] => [1,4,3,5,2] => [3,1,1]
 => [1,1]
 => 1
[4,2,1,3,5] => [1,4,3,2,5] => [3,1,1]
 => [1,1]
 => 1
[4,2,1,5,3] => [1,4,5,3,2] => [3,1,1]
 => [1,1]
 => 1
[4,2,3,5,1] => [1,4,5,2,3] => [3,2]
 => [2]
 => 2
[4,2,5,3,1] => [1,4,3,5,2] => [3,1,1]
 => [1,1]
 => 1
[4,3,1,5,2] => [1,4,5,2,3] => [3,2]
 => [2]
 => 2
[4,3,2,5,1] => [1,4,5,2,3] => [3,2]
 => [2]
 => 2
[4,5,1,2,3] => [1,4,2,5,3] => [3,2]
 => [2]
 => 2
[4,5,1,3,2] => [1,4,3,2,5] => [3,1,1]
 => [1,1]
 => 1
[4,5,2,1,3] => [1,4,2,5,3] => [3,2]
 => [2]
 => 2
[4,5,2,3,1] => [1,4,3,2,5] => [3,1,1]
 => [1,1]
 => 1
[4,5,3,1,2] => [1,4,2,5,3] => [3,2]
 => [2]
 => 2
[4,5,3,2,1] => [1,4,2,5,3] => [3,2]
 => [2]
 => 2
[5,1,2,3,4] => [1,5,4,3,2] => [2,1,1,1]
 => [1,1,1]
 => 1
[5,1,2,4,3] => [1,5,3,2,4] => [3,1,1]
 => [1,1]
 => 1
[5,1,3,2,4] => [1,5,4,2,3] => [3,1,1]
 => [1,1]
 => 1
[5,1,4,2,3] => [1,5,3,4,2] => [3,1,1]
 => [1,1]
 => 1
[5,2,1,3,4] => [1,5,4,3,2] => [2,1,1,1]
 => [1,1,1]
 => 1
[5,2,1,4,3] => [1,5,3,2,4] => [3,1,1]
 => [1,1]
 => 1
[5,2,3,1,4] => [1,5,4,2,3] => [3,1,1]
 => [1,1]
 => 1
[5,2,4,1,3] => [1,5,3,4,2] => [3,1,1]
 => [1,1]
 => 1
[5,3,1,2,4] => [1,5,4,2,3] => [3,1,1]
 => [1,1]
 => 1
[5,3,2,1,4] => [1,5,4,2,3] => [3,1,1]
 => [1,1]
 => 1
[5,4,1,2,3] => [1,5,3,2,4] => [3,1,1]
 => [1,1]
 => 1
[5,4,1,3,2] => [1,5,2,4,3] => [3,1,1]
 => [1,1]
 => 1
[5,4,2,1,3] => [1,5,3,2,4] => [3,1,1]
 => [1,1]
 => 1
[5,4,2,3,1] => [1,5,2,4,3] => [3,1,1]
 => [1,1]
 => 1
[5,4,3,1,2] => [1,5,2,4,3] => [3,1,1]
 => [1,1]
 => 1
[5,4,3,2,1] => [1,5,2,4,3] => [3,1,1]
 => [1,1]
 => 1
[1,2,6,3,4,5] => [1,2,3,6,5,4] => [4,1,1]
 => [1,1]
 => 1
[1,2,6,4,3,5] => [1,2,3,6,5,4] => [4,1,1]
 => [1,1]
 => 1

Description

The least common multiple of the parts of the partition.

Matching statistic: St000707
(load all 5 compositions to match this statistic)

Mapping

Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000707: Integer partitions ⟶ ℤResult quality: 62% ●values known / values provided: 62%●distinct values known / distinct values provided: 67%

Values

[1] => [1] => [1]
 => []
 => ? = 0
[1,2] => [1,2] => [2]
 => []
 => ? ∊ {0,0}
[2,1] => [1,2] => [2]
 => []
 => ? ∊ {0,0}
[1,2,3] => [1,2,3] => [3]
 => []
 => ? ∊ {0,0,1,1,1,1}
[1,3,2] => [1,2,3] => [3]
 => []
 => ? ∊ {0,0,1,1,1,1}
[2,1,3] => [1,2,3] => [3]
 => []
 => ? ∊ {0,0,1,1,1,1}
[2,3,1] => [1,2,3] => [3]
 => []
 => ? ∊ {0,0,1,1,1,1}
[3,1,2] => [1,3,2] => [2,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1}
[3,2,1] => [1,3,2] => [2,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1}
[1,2,3,4] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[1,2,4,3] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[1,3,2,4] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[1,3,4,2] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[1,4,2,3] => [1,2,4,3] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[1,4,3,2] => [1,2,4,3] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[2,1,3,4] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[2,1,4,3] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[2,3,1,4] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[2,3,4,1] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[2,4,1,3] => [1,2,4,3] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[2,4,3,1] => [1,2,4,3] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[3,1,2,4] => [1,3,2,4] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[3,1,4,2] => [1,3,4,2] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[3,2,1,4] => [1,3,2,4] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[3,2,4,1] => [1,3,4,2] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[3,4,1,2] => [1,3,2,4] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[3,4,2,1] => [1,3,2,4] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[4,1,2,3] => [1,4,3,2] => [2,1,1]
 => [1,1]
 => 1
[4,1,3,2] => [1,4,2,3] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[4,2,1,3] => [1,4,3,2] => [2,1,1]
 => [1,1]
 => 1
[4,2,3,1] => [1,4,2,3] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[4,3,1,2] => [1,4,2,3] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[4,3,2,1] => [1,4,2,3] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[1,2,3,4,5] => [1,2,3,4,5] => [5]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,2,3,5,4] => [1,2,3,4,5] => [5]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,2,4,3,5] => [1,2,3,4,5] => [5]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,2,4,5,3] => [1,2,3,4,5] => [5]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,2,5,3,4] => [1,2,3,5,4] => [4,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,2,5,4,3] => [1,2,3,5,4] => [4,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,3,2,4,5] => [1,2,3,4,5] => [5]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,3,2,5,4] => [1,2,3,4,5] => [5]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,3,4,2,5] => [1,2,3,4,5] => [5]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,3,4,5,2] => [1,2,3,4,5] => [5]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,3,5,2,4] => [1,2,3,5,4] => [4,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,3,5,4,2] => [1,2,3,5,4] => [4,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,4,2,3,5] => [1,2,4,3,5] => [4,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,4,2,5,3] => [1,2,4,5,3] => [4,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,4,3,2,5] => [1,2,4,3,5] => [4,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,4,3,5,2] => [1,2,4,5,3] => [4,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,4,5,2,3] => [1,2,4,3,5] => [4,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,4,5,3,2] => [1,2,4,3,5] => [4,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,5,2,3,4] => [1,2,5,4,3] => [3,1,1]
 => [1,1]
 => 1
[1,5,2,4,3] => [1,2,5,3,4] => [4,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,5,3,2,4] => [1,2,5,4,3] => [3,1,1]
 => [1,1]
 => 1
[2,5,1,3,4] => [1,2,5,4,3] => [3,1,1]
 => [1,1]
 => 1
[2,5,3,1,4] => [1,2,5,4,3] => [3,1,1]
 => [1,1]
 => 1
[3,1,5,2,4] => [1,3,5,4,2] => [3,1,1]
 => [1,1]
 => 1
[3,1,5,4,2] => [1,3,5,2,4] => [3,2]
 => [2]
 => 2
[3,2,5,1,4] => [1,3,5,4,2] => [3,1,1]
 => [1,1]
 => 1
[3,2,5,4,1] => [1,3,5,2,4] => [3,2]
 => [2]
 => 2
[3,4,5,1,2] => [1,3,5,2,4] => [3,2]
 => [2]
 => 2
[3,4,5,2,1] => [1,3,5,2,4] => [3,2]
 => [2]
 => 2
[3,5,1,2,4] => [1,3,2,5,4] => [3,2]
 => [2]
 => 2
[3,5,1,4,2] => [1,3,2,5,4] => [3,2]
 => [2]
 => 2
[3,5,2,1,4] => [1,3,2,5,4] => [3,2]
 => [2]
 => 2
[3,5,2,4,1] => [1,3,2,5,4] => [3,2]
 => [2]
 => 2
[4,1,2,3,5] => [1,4,3,2,5] => [3,1,1]
 => [1,1]
 => 1
[4,1,2,5,3] => [1,4,5,3,2] => [3,1,1]
 => [1,1]
 => 1
[4,1,3,5,2] => [1,4,5,2,3] => [3,2]
 => [2]
 => 2
[4,1,5,3,2] => [1,4,3,5,2] => [3,1,1]
 => [1,1]
 => 1
[4,2,1,3,5] => [1,4,3,2,5] => [3,1,1]
 => [1,1]
 => 1
[4,2,1,5,3] => [1,4,5,3,2] => [3,1,1]
 => [1,1]
 => 1
[4,2,3,5,1] => [1,4,5,2,3] => [3,2]
 => [2]
 => 2
[4,2,5,3,1] => [1,4,3,5,2] => [3,1,1]
 => [1,1]
 => 1
[4,3,1,5,2] => [1,4,5,2,3] => [3,2]
 => [2]
 => 2
[4,3,2,5,1] => [1,4,5,2,3] => [3,2]
 => [2]
 => 2
[4,5,1,2,3] => [1,4,2,5,3] => [3,2]
 => [2]
 => 2
[4,5,1,3,2] => [1,4,3,2,5] => [3,1,1]
 => [1,1]
 => 1
[4,5,2,1,3] => [1,4,2,5,3] => [3,2]
 => [2]
 => 2
[4,5,2,3,1] => [1,4,3,2,5] => [3,1,1]
 => [1,1]
 => 1
[4,5,3,1,2] => [1,4,2,5,3] => [3,2]
 => [2]
 => 2
[4,5,3,2,1] => [1,4,2,5,3] => [3,2]
 => [2]
 => 2
[5,1,2,3,4] => [1,5,4,3,2] => [2,1,1,1]
 => [1,1,1]
 => 1
[5,1,2,4,3] => [1,5,3,2,4] => [3,1,1]
 => [1,1]
 => 1
[5,1,3,2,4] => [1,5,4,2,3] => [3,1,1]
 => [1,1]
 => 1
[5,1,4,2,3] => [1,5,3,4,2] => [3,1,1]
 => [1,1]
 => 1
[5,2,1,3,4] => [1,5,4,3,2] => [2,1,1,1]
 => [1,1,1]
 => 1
[5,2,1,4,3] => [1,5,3,2,4] => [3,1,1]
 => [1,1]
 => 1
[5,2,3,1,4] => [1,5,4,2,3] => [3,1,1]
 => [1,1]
 => 1
[5,2,4,1,3] => [1,5,3,4,2] => [3,1,1]
 => [1,1]
 => 1
[5,3,1,2,4] => [1,5,4,2,3] => [3,1,1]
 => [1,1]
 => 1
[5,3,2,1,4] => [1,5,4,2,3] => [3,1,1]
 => [1,1]
 => 1
[5,4,1,2,3] => [1,5,3,2,4] => [3,1,1]
 => [1,1]
 => 1
[5,4,1,3,2] => [1,5,2,4,3] => [3,1,1]
 => [1,1]
 => 1
[5,4,2,1,3] => [1,5,3,2,4] => [3,1,1]
 => [1,1]
 => 1
[5,4,2,3,1] => [1,5,2,4,3] => [3,1,1]
 => [1,1]
 => 1
[5,4,3,1,2] => [1,5,2,4,3] => [3,1,1]
 => [1,1]
 => 1
[5,4,3,2,1] => [1,5,2,4,3] => [3,1,1]
 => [1,1]
 => 1
[1,2,6,3,4,5] => [1,2,3,6,5,4] => [4,1,1]
 => [1,1]
 => 1
[1,2,6,4,3,5] => [1,2,3,6,5,4] => [4,1,1]
 => [1,1]
 => 1

Description

The product of the factorials of the parts.

Matching statistic: St000708
(load all 5 compositions to match this statistic)

Mapping

Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000708: Integer partitions ⟶ ℤResult quality: 62% ●values known / values provided: 62%●distinct values known / distinct values provided: 67%

Values

[1] => [1] => [1]
 => []
 => ? = 0
[1,2] => [1,2] => [2]
 => []
 => ? ∊ {0,0}
[2,1] => [1,2] => [2]
 => []
 => ? ∊ {0,0}
[1,2,3] => [1,2,3] => [3]
 => []
 => ? ∊ {0,0,1,1,1,1}
[1,3,2] => [1,2,3] => [3]
 => []
 => ? ∊ {0,0,1,1,1,1}
[2,1,3] => [1,2,3] => [3]
 => []
 => ? ∊ {0,0,1,1,1,1}
[2,3,1] => [1,2,3] => [3]
 => []
 => ? ∊ {0,0,1,1,1,1}
[3,1,2] => [1,3,2] => [2,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1}
[3,2,1] => [1,3,2] => [2,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1}
[1,2,3,4] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[1,2,4,3] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[1,3,2,4] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[1,3,4,2] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[1,4,2,3] => [1,2,4,3] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[1,4,3,2] => [1,2,4,3] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[2,1,3,4] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[2,1,4,3] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[2,3,1,4] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[2,3,4,1] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[2,4,1,3] => [1,2,4,3] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[2,4,3,1] => [1,2,4,3] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[3,1,2,4] => [1,3,2,4] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[3,1,4,2] => [1,3,4,2] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[3,2,1,4] => [1,3,2,4] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[3,2,4,1] => [1,3,4,2] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[3,4,1,2] => [1,3,2,4] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[3,4,2,1] => [1,3,2,4] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[4,1,2,3] => [1,4,3,2] => [2,1,1]
 => [1,1]
 => 1
[4,1,3,2] => [1,4,2,3] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[4,2,1,3] => [1,4,3,2] => [2,1,1]
 => [1,1]
 => 1
[4,2,3,1] => [1,4,2,3] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[4,3,1,2] => [1,4,2,3] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[4,3,2,1] => [1,4,2,3] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[1,2,3,4,5] => [1,2,3,4,5] => [5]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,2,3,5,4] => [1,2,3,4,5] => [5]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,2,4,3,5] => [1,2,3,4,5] => [5]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,2,4,5,3] => [1,2,3,4,5] => [5]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,2,5,3,4] => [1,2,3,5,4] => [4,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,2,5,4,3] => [1,2,3,5,4] => [4,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,3,2,4,5] => [1,2,3,4,5] => [5]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,3,2,5,4] => [1,2,3,4,5] => [5]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,3,4,2,5] => [1,2,3,4,5] => [5]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,3,4,5,2] => [1,2,3,4,5] => [5]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,3,5,2,4] => [1,2,3,5,4] => [4,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,3,5,4,2] => [1,2,3,5,4] => [4,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,4,2,3,5] => [1,2,4,3,5] => [4,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,4,2,5,3] => [1,2,4,5,3] => [4,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,4,3,2,5] => [1,2,4,3,5] => [4,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,4,3,5,2] => [1,2,4,5,3] => [4,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,4,5,2,3] => [1,2,4,3,5] => [4,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,4,5,3,2] => [1,2,4,3,5] => [4,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,5,2,3,4] => [1,2,5,4,3] => [3,1,1]
 => [1,1]
 => 1
[1,5,2,4,3] => [1,2,5,3,4] => [4,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,5,3,2,4] => [1,2,5,4,3] => [3,1,1]
 => [1,1]
 => 1
[2,5,1,3,4] => [1,2,5,4,3] => [3,1,1]
 => [1,1]
 => 1
[2,5,3,1,4] => [1,2,5,4,3] => [3,1,1]
 => [1,1]
 => 1
[3,1,5,2,4] => [1,3,5,4,2] => [3,1,1]
 => [1,1]
 => 1
[3,1,5,4,2] => [1,3,5,2,4] => [3,2]
 => [2]
 => 2
[3,2,5,1,4] => [1,3,5,4,2] => [3,1,1]
 => [1,1]
 => 1
[3,2,5,4,1] => [1,3,5,2,4] => [3,2]
 => [2]
 => 2
[3,4,5,1,2] => [1,3,5,2,4] => [3,2]
 => [2]
 => 2
[3,4,5,2,1] => [1,3,5,2,4] => [3,2]
 => [2]
 => 2
[3,5,1,2,4] => [1,3,2,5,4] => [3,2]
 => [2]
 => 2
[3,5,1,4,2] => [1,3,2,5,4] => [3,2]
 => [2]
 => 2
[3,5,2,1,4] => [1,3,2,5,4] => [3,2]
 => [2]
 => 2
[3,5,2,4,1] => [1,3,2,5,4] => [3,2]
 => [2]
 => 2
[4,1,2,3,5] => [1,4,3,2,5] => [3,1,1]
 => [1,1]
 => 1
[4,1,2,5,3] => [1,4,5,3,2] => [3,1,1]
 => [1,1]
 => 1
[4,1,3,5,2] => [1,4,5,2,3] => [3,2]
 => [2]
 => 2
[4,1,5,3,2] => [1,4,3,5,2] => [3,1,1]
 => [1,1]
 => 1
[4,2,1,3,5] => [1,4,3,2,5] => [3,1,1]
 => [1,1]
 => 1
[4,2,1,5,3] => [1,4,5,3,2] => [3,1,1]
 => [1,1]
 => 1
[4,2,3,5,1] => [1,4,5,2,3] => [3,2]
 => [2]
 => 2
[4,2,5,3,1] => [1,4,3,5,2] => [3,1,1]
 => [1,1]
 => 1
[4,3,1,5,2] => [1,4,5,2,3] => [3,2]
 => [2]
 => 2
[4,3,2,5,1] => [1,4,5,2,3] => [3,2]
 => [2]
 => 2
[4,5,1,2,3] => [1,4,2,5,3] => [3,2]
 => [2]
 => 2
[4,5,1,3,2] => [1,4,3,2,5] => [3,1,1]
 => [1,1]
 => 1
[4,5,2,1,3] => [1,4,2,5,3] => [3,2]
 => [2]
 => 2
[4,5,2,3,1] => [1,4,3,2,5] => [3,1,1]
 => [1,1]
 => 1
[4,5,3,1,2] => [1,4,2,5,3] => [3,2]
 => [2]
 => 2
[4,5,3,2,1] => [1,4,2,5,3] => [3,2]
 => [2]
 => 2
[5,1,2,3,4] => [1,5,4,3,2] => [2,1,1,1]
 => [1,1,1]
 => 1
[5,1,2,4,3] => [1,5,3,2,4] => [3,1,1]
 => [1,1]
 => 1
[5,1,3,2,4] => [1,5,4,2,3] => [3,1,1]
 => [1,1]
 => 1
[5,1,4,2,3] => [1,5,3,4,2] => [3,1,1]
 => [1,1]
 => 1
[5,2,1,3,4] => [1,5,4,3,2] => [2,1,1,1]
 => [1,1,1]
 => 1
[5,2,1,4,3] => [1,5,3,2,4] => [3,1,1]
 => [1,1]
 => 1
[5,2,3,1,4] => [1,5,4,2,3] => [3,1,1]
 => [1,1]
 => 1
[5,2,4,1,3] => [1,5,3,4,2] => [3,1,1]
 => [1,1]
 => 1
[5,3,1,2,4] => [1,5,4,2,3] => [3,1,1]
 => [1,1]
 => 1
[5,3,2,1,4] => [1,5,4,2,3] => [3,1,1]
 => [1,1]
 => 1
[5,4,1,2,3] => [1,5,3,2,4] => [3,1,1]
 => [1,1]
 => 1
[5,4,1,3,2] => [1,5,2,4,3] => [3,1,1]
 => [1,1]
 => 1
[5,4,2,1,3] => [1,5,3,2,4] => [3,1,1]
 => [1,1]
 => 1
[5,4,2,3,1] => [1,5,2,4,3] => [3,1,1]
 => [1,1]
 => 1
[5,4,3,1,2] => [1,5,2,4,3] => [3,1,1]
 => [1,1]
 => 1
[5,4,3,2,1] => [1,5,2,4,3] => [3,1,1]
 => [1,1]
 => 1
[1,2,6,3,4,5] => [1,2,3,6,5,4] => [4,1,1]
 => [1,1]
 => 1
[1,2,6,4,3,5] => [1,2,3,6,5,4] => [4,1,1]
 => [1,1]
 => 1

Description

The product of the parts of an integer partition.

Matching statistic: St000933
(load all 5 compositions to match this statistic)

Mapping

Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000933: Integer partitions ⟶ ℤResult quality: 62% ●values known / values provided: 62%●distinct values known / distinct values provided: 67%

Values

[1] => [1] => [1]
 => []
 => ? = 0
[1,2] => [1,2] => [2]
 => []
 => ? ∊ {0,0}
[2,1] => [1,2] => [2]
 => []
 => ? ∊ {0,0}
[1,2,3] => [1,2,3] => [3]
 => []
 => ? ∊ {0,0,1,1,1,1}
[1,3,2] => [1,2,3] => [3]
 => []
 => ? ∊ {0,0,1,1,1,1}
[2,1,3] => [1,2,3] => [3]
 => []
 => ? ∊ {0,0,1,1,1,1}
[2,3,1] => [1,2,3] => [3]
 => []
 => ? ∊ {0,0,1,1,1,1}
[3,1,2] => [1,3,2] => [2,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1}
[3,2,1] => [1,3,2] => [2,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1}
[1,2,3,4] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[1,2,4,3] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[1,3,2,4] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[1,3,4,2] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[1,4,2,3] => [1,2,4,3] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[1,4,3,2] => [1,2,4,3] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[2,1,3,4] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[2,1,4,3] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[2,3,1,4] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[2,3,4,1] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[2,4,1,3] => [1,2,4,3] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[2,4,3,1] => [1,2,4,3] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[3,1,2,4] => [1,3,2,4] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[3,1,4,2] => [1,3,4,2] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[3,2,1,4] => [1,3,2,4] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[3,2,4,1] => [1,3,4,2] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[3,4,1,2] => [1,3,2,4] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[3,4,2,1] => [1,3,2,4] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[4,1,2,3] => [1,4,3,2] => [2,1,1]
 => [1,1]
 => 1
[4,1,3,2] => [1,4,2,3] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[4,2,1,3] => [1,4,3,2] => [2,1,1]
 => [1,1]
 => 1
[4,2,3,1] => [1,4,2,3] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[4,3,1,2] => [1,4,2,3] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[4,3,2,1] => [1,4,2,3] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[1,2,3,4,5] => [1,2,3,4,5] => [5]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,2,3,5,4] => [1,2,3,4,5] => [5]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,2,4,3,5] => [1,2,3,4,5] => [5]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,2,4,5,3] => [1,2,3,4,5] => [5]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,2,5,3,4] => [1,2,3,5,4] => [4,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,2,5,4,3] => [1,2,3,5,4] => [4,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,3,2,4,5] => [1,2,3,4,5] => [5]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,3,2,5,4] => [1,2,3,4,5] => [5]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,3,4,2,5] => [1,2,3,4,5] => [5]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,3,4,5,2] => [1,2,3,4,5] => [5]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,3,5,2,4] => [1,2,3,5,4] => [4,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,3,5,4,2] => [1,2,3,5,4] => [4,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,4,2,3,5] => [1,2,4,3,5] => [4,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,4,2,5,3] => [1,2,4,5,3] => [4,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,4,3,2,5] => [1,2,4,3,5] => [4,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,4,3,5,2] => [1,2,4,5,3] => [4,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,4,5,2,3] => [1,2,4,3,5] => [4,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,4,5,3,2] => [1,2,4,3,5] => [4,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,5,2,3,4] => [1,2,5,4,3] => [3,1,1]
 => [1,1]
 => 1
[1,5,2,4,3] => [1,2,5,3,4] => [4,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,5,3,2,4] => [1,2,5,4,3] => [3,1,1]
 => [1,1]
 => 1
[2,5,1,3,4] => [1,2,5,4,3] => [3,1,1]
 => [1,1]
 => 1
[2,5,3,1,4] => [1,2,5,4,3] => [3,1,1]
 => [1,1]
 => 1
[3,1,5,2,4] => [1,3,5,4,2] => [3,1,1]
 => [1,1]
 => 1
[3,1,5,4,2] => [1,3,5,2,4] => [3,2]
 => [2]
 => 2
[3,2,5,1,4] => [1,3,5,4,2] => [3,1,1]
 => [1,1]
 => 1
[3,2,5,4,1] => [1,3,5,2,4] => [3,2]
 => [2]
 => 2
[3,4,5,1,2] => [1,3,5,2,4] => [3,2]
 => [2]
 => 2
[3,4,5,2,1] => [1,3,5,2,4] => [3,2]
 => [2]
 => 2
[3,5,1,2,4] => [1,3,2,5,4] => [3,2]
 => [2]
 => 2
[3,5,1,4,2] => [1,3,2,5,4] => [3,2]
 => [2]
 => 2
[3,5,2,1,4] => [1,3,2,5,4] => [3,2]
 => [2]
 => 2
[3,5,2,4,1] => [1,3,2,5,4] => [3,2]
 => [2]
 => 2
[4,1,2,3,5] => [1,4,3,2,5] => [3,1,1]
 => [1,1]
 => 1
[4,1,2,5,3] => [1,4,5,3,2] => [3,1,1]
 => [1,1]
 => 1
[4,1,3,5,2] => [1,4,5,2,3] => [3,2]
 => [2]
 => 2
[4,1,5,3,2] => [1,4,3,5,2] => [3,1,1]
 => [1,1]
 => 1
[4,2,1,3,5] => [1,4,3,2,5] => [3,1,1]
 => [1,1]
 => 1
[4,2,1,5,3] => [1,4,5,3,2] => [3,1,1]
 => [1,1]
 => 1
[4,2,3,5,1] => [1,4,5,2,3] => [3,2]
 => [2]
 => 2
[4,2,5,3,1] => [1,4,3,5,2] => [3,1,1]
 => [1,1]
 => 1
[4,3,1,5,2] => [1,4,5,2,3] => [3,2]
 => [2]
 => 2
[4,3,2,5,1] => [1,4,5,2,3] => [3,2]
 => [2]
 => 2
[4,5,1,2,3] => [1,4,2,5,3] => [3,2]
 => [2]
 => 2
[4,5,1,3,2] => [1,4,3,2,5] => [3,1,1]
 => [1,1]
 => 1
[4,5,2,1,3] => [1,4,2,5,3] => [3,2]
 => [2]
 => 2
[4,5,2,3,1] => [1,4,3,2,5] => [3,1,1]
 => [1,1]
 => 1
[4,5,3,1,2] => [1,4,2,5,3] => [3,2]
 => [2]
 => 2
[4,5,3,2,1] => [1,4,2,5,3] => [3,2]
 => [2]
 => 2
[5,1,2,3,4] => [1,5,4,3,2] => [2,1,1,1]
 => [1,1,1]
 => 1
[5,1,2,4,3] => [1,5,3,2,4] => [3,1,1]
 => [1,1]
 => 1
[5,1,3,2,4] => [1,5,4,2,3] => [3,1,1]
 => [1,1]
 => 1
[5,1,4,2,3] => [1,5,3,4,2] => [3,1,1]
 => [1,1]
 => 1
[5,2,1,3,4] => [1,5,4,3,2] => [2,1,1,1]
 => [1,1,1]
 => 1
[5,2,1,4,3] => [1,5,3,2,4] => [3,1,1]
 => [1,1]
 => 1
[5,2,3,1,4] => [1,5,4,2,3] => [3,1,1]
 => [1,1]
 => 1
[5,2,4,1,3] => [1,5,3,4,2] => [3,1,1]
 => [1,1]
 => 1
[5,3,1,2,4] => [1,5,4,2,3] => [3,1,1]
 => [1,1]
 => 1
[5,3,2,1,4] => [1,5,4,2,3] => [3,1,1]
 => [1,1]
 => 1
[5,4,1,2,3] => [1,5,3,2,4] => [3,1,1]
 => [1,1]
 => 1
[5,4,1,3,2] => [1,5,2,4,3] => [3,1,1]
 => [1,1]
 => 1
[5,4,2,1,3] => [1,5,3,2,4] => [3,1,1]
 => [1,1]
 => 1
[5,4,2,3,1] => [1,5,2,4,3] => [3,1,1]
 => [1,1]
 => 1
[5,4,3,1,2] => [1,5,2,4,3] => [3,1,1]
 => [1,1]
 => 1
[5,4,3,2,1] => [1,5,2,4,3] => [3,1,1]
 => [1,1]
 => 1
[1,2,6,3,4,5] => [1,2,3,6,5,4] => [4,1,1]
 => [1,1]
 => 1
[1,2,6,4,3,5] => [1,2,3,6,5,4] => [4,1,1]
 => [1,1]
 => 1

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: St000259

Mapping

Mp00252: Permutations —restriction⟶ Permutations
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000259: Graphs ⟶ ℤResult quality: 58% ●values known / values provided: 58%●distinct values known / distinct values provided: 100%

Values

[1] => [] => [] => ([],0)
 => ? = 0
[1,2] => [1] => [1] => ([],1)
 => 0
[2,1] => [1] => [1] => ([],1)
 => 0
[1,2,3] => [1,2] => [1,2] => ([],2)
 => ? ∊ {0,0,1}
[1,3,2] => [1,2] => [1,2] => ([],2)
 => ? ∊ {0,0,1}
[2,1,3] => [2,1] => [2,1] => ([(0,1)],2)
 => 1
[2,3,1] => [2,1] => [2,1] => ([(0,1)],2)
 => 1
[3,1,2] => [1,2] => [1,2] => ([],2)
 => ? ∊ {0,0,1}
[3,2,1] => [2,1] => [2,1] => ([(0,1)],2)
 => 1
[1,2,3,4] => [1,2,3] => [1,2,3] => ([],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1}
[1,2,4,3] => [1,2,3] => [1,2,3] => ([],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1}
[1,3,2,4] => [1,3,2] => [1,3,2] => ([(1,2)],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1}
[1,3,4,2] => [1,3,2] => [1,3,2] => ([(1,2)],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1}
[1,4,2,3] => [1,2,3] => [1,2,3] => ([],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1}
[1,4,3,2] => [1,3,2] => [1,3,2] => ([(1,2)],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1}
[2,1,3,4] => [2,1,3] => [2,1,3] => ([(1,2)],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1}
[2,1,4,3] => [2,1,3] => [2,1,3] => ([(1,2)],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1}
[2,3,1,4] => [2,3,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
 => 1
[2,3,4,1] => [2,3,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
 => 1
[2,4,1,3] => [2,1,3] => [2,1,3] => ([(1,2)],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1}
[2,4,3,1] => [2,3,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
 => 1
[3,1,2,4] => [3,1,2] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
 => 1
[3,1,4,2] => [3,1,2] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
 => 1
[3,2,1,4] => [3,2,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
 => 1
[3,2,4,1] => [3,2,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
 => 1
[3,4,1,2] => [3,1,2] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
 => 1
[3,4,2,1] => [3,2,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
 => 1
[4,1,2,3] => [1,2,3] => [1,2,3] => ([],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1}
[4,1,3,2] => [1,3,2] => [1,3,2] => ([(1,2)],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1}
[4,2,1,3] => [2,1,3] => [2,1,3] => ([(1,2)],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1}
[4,2,3,1] => [2,3,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
 => 1
[4,3,1,2] => [3,1,2] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
 => 1
[4,3,2,1] => [3,2,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
 => 1
[1,2,3,4,5] => [1,2,3,4] => [1,2,3,4] => ([],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2}
[1,2,3,5,4] => [1,2,3,4] => [1,2,3,4] => ([],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2}
[1,2,4,3,5] => [1,2,4,3] => [1,2,4,3] => ([(2,3)],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2}
[1,2,4,5,3] => [1,2,4,3] => [1,2,4,3] => ([(2,3)],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2}
[1,2,5,3,4] => [1,2,3,4] => [1,2,3,4] => ([],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2}
[1,2,5,4,3] => [1,2,4,3] => [1,2,4,3] => ([(2,3)],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2}
[1,3,2,4,5] => [1,3,2,4] => [1,3,2,4] => ([(2,3)],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2}
[1,3,2,5,4] => [1,3,2,4] => [1,3,2,4] => ([(2,3)],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2}
[1,3,4,2,5] => [1,3,4,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2}
[1,3,4,5,2] => [1,3,4,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2}
[1,3,5,2,4] => [1,3,2,4] => [1,3,2,4] => ([(2,3)],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2}
[1,3,5,4,2] => [1,3,4,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2}
[1,4,2,3,5] => [1,4,2,3] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2}
[1,4,2,5,3] => [1,4,2,3] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2}
[1,4,3,2,5] => [1,4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2}
[1,4,3,5,2] => [1,4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2}
[1,4,5,2,3] => [1,4,2,3] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2}
[1,4,5,3,2] => [1,4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2}
[1,5,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2}
[1,5,2,4,3] => [1,2,4,3] => [1,2,4,3] => ([(2,3)],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2}
[1,5,3,2,4] => [1,3,2,4] => [1,3,2,4] => ([(2,3)],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2}
[1,5,3,4,2] => [1,3,4,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2}
[1,5,4,2,3] => [1,4,2,3] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2}
[1,5,4,3,2] => [1,4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2}
[2,1,3,4,5] => [2,1,3,4] => [2,1,3,4] => ([(2,3)],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2}
[2,1,3,5,4] => [2,1,3,4] => [2,1,3,4] => ([(2,3)],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2}
[2,1,4,3,5] => [2,1,4,3] => [2,1,4,3] => ([(0,3),(1,2)],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2}
[2,1,4,5,3] => [2,1,4,3] => [2,1,4,3] => ([(0,3),(1,2)],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2}
[2,1,5,3,4] => [2,1,3,4] => [2,1,3,4] => ([(2,3)],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2}
[2,1,5,4,3] => [2,1,4,3] => [2,1,4,3] => ([(0,3),(1,2)],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2}
[2,3,1,4,5] => [2,3,1,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2}
[2,3,1,5,4] => [2,3,1,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2}
[2,3,4,1,5] => [2,3,4,1] => [4,2,3,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
[2,3,4,5,1] => [2,3,4,1] => [4,2,3,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
[2,3,5,1,4] => [2,3,1,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2}
[2,3,5,4,1] => [2,3,4,1] => [4,2,3,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
[2,4,1,3,5] => [2,4,1,3] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2
[2,4,1,5,3] => [2,4,1,3] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2
[2,4,3,1,5] => [2,4,3,1] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
[2,4,3,5,1] => [2,4,3,1] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
[2,4,5,1,3] => [2,4,1,3] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2
[2,4,5,3,1] => [2,4,3,1] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
[2,5,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(2,3)],4)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2}
[2,5,3,4,1] => [2,3,4,1] => [4,2,3,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
[2,5,4,1,3] => [2,4,1,3] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2
[2,5,4,3,1] => [2,4,3,1] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
[3,1,4,2,5] => [3,1,4,2] => [4,2,3,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
[3,1,4,5,2] => [3,1,4,2] => [4,2,3,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
[3,1,5,4,2] => [3,1,4,2] => [4,2,3,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
[3,2,4,1,5] => [3,2,4,1] => [4,2,3,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
[3,2,4,5,1] => [3,2,4,1] => [4,2,3,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
[3,2,5,4,1] => [3,2,4,1] => [4,2,3,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
[3,4,1,2,5] => [3,4,1,2] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
[3,4,1,5,2] => [3,4,1,2] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
[3,4,2,1,5] => [3,4,2,1] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
[3,4,2,5,1] => [3,4,2,1] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
[3,4,5,1,2] => [3,4,1,2] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
[3,4,5,2,1] => [3,4,2,1] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
[3,5,1,4,2] => [3,1,4,2] => [4,2,3,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
[3,5,2,4,1] => [3,2,4,1] => [4,2,3,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
[3,5,4,1,2] => [3,4,1,2] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
[3,5,4,2,1] => [3,4,2,1] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
[4,1,2,3,5] => [4,1,2,3] => [4,2,3,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
[4,1,2,5,3] => [4,1,2,3] => [4,2,3,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
[4,1,3,2,5] => [4,1,3,2] => [4,2,3,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
[4,1,3,5,2] => [4,1,3,2] => [4,2,3,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
[4,1,5,2,3] => [4,1,2,3] => [4,2,3,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2

Description

The diameter of a connected graph. This is the greatest distance between any pair of vertices.

Matching statistic: St001630
(load all 4 compositions to match this statistic)

Mapping

Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00180: Integer compositions —to ribbon⟶ Skew partitions
Mp00192: Skew partitions —dominating sublattice⟶ Lattices
St001630: Lattices ⟶ ℤResult quality: 56% ●values known / values provided: 56%●distinct values known / distinct values provided: 67%

Values

[1] => [1] => [[1],[]]
 => ([],1)
 => ? = 0
[1,2] => [2] => [[2],[]]
 => ([],1)
 => ? ∊ {0,0}
[2,1] => [1,1] => [[1,1],[]]
 => ([],1)
 => ? ∊ {0,0}
[1,2,3] => [3] => [[3],[]]
 => ([],1)
 => ? ∊ {0,0,1,1,1,1}
[1,3,2] => [2,1] => [[2,2],[1]]
 => ([],1)
 => ? ∊ {0,0,1,1,1,1}
[2,1,3] => [1,2] => [[2,1],[]]
 => ([],1)
 => ? ∊ {0,0,1,1,1,1}
[2,3,1] => [2,1] => [[2,2],[1]]
 => ([],1)
 => ? ∊ {0,0,1,1,1,1}
[3,1,2] => [1,2] => [[2,1],[]]
 => ([],1)
 => ? ∊ {0,0,1,1,1,1}
[3,2,1] => [1,1,1] => [[1,1,1],[]]
 => ([],1)
 => ? ∊ {0,0,1,1,1,1}
[1,2,3,4] => [4] => [[4],[]]
 => ([],1)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[1,2,4,3] => [3,1] => [[3,3],[2]]
 => ([],1)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[1,3,2,4] => [2,2] => [[3,2],[1]]
 => ([(0,1)],2)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[1,3,4,2] => [3,1] => [[3,3],[2]]
 => ([],1)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[1,4,2,3] => [2,2] => [[3,2],[1]]
 => ([(0,1)],2)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[1,4,3,2] => [2,1,1] => [[2,2,2],[1,1]]
 => ([],1)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[2,1,3,4] => [1,3] => [[3,1],[]]
 => ([],1)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[2,1,4,3] => [1,2,1] => [[2,2,1],[1]]
 => ([(0,1)],2)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[2,3,1,4] => [2,2] => [[3,2],[1]]
 => ([(0,1)],2)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[2,3,4,1] => [3,1] => [[3,3],[2]]
 => ([],1)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[2,4,1,3] => [2,2] => [[3,2],[1]]
 => ([(0,1)],2)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[2,4,3,1] => [2,1,1] => [[2,2,2],[1,1]]
 => ([],1)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[3,1,2,4] => [1,3] => [[3,1],[]]
 => ([],1)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[3,1,4,2] => [1,2,1] => [[2,2,1],[1]]
 => ([(0,1)],2)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[3,2,1,4] => [1,1,2] => [[2,1,1],[]]
 => ([],1)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[3,2,4,1] => [1,2,1] => [[2,2,1],[1]]
 => ([(0,1)],2)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[3,4,1,2] => [2,2] => [[3,2],[1]]
 => ([(0,1)],2)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[3,4,2,1] => [2,1,1] => [[2,2,2],[1,1]]
 => ([],1)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[4,1,2,3] => [1,3] => [[3,1],[]]
 => ([],1)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[4,1,3,2] => [1,2,1] => [[2,2,1],[1]]
 => ([(0,1)],2)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[4,2,1,3] => [1,1,2] => [[2,1,1],[]]
 => ([],1)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[4,2,3,1] => [1,2,1] => [[2,2,1],[1]]
 => ([(0,1)],2)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[4,3,1,2] => [1,1,2] => [[2,1,1],[]]
 => ([],1)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[4,3,2,1] => [1,1,1,1] => [[1,1,1,1],[]]
 => ([],1)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[1,2,3,4,5] => [5] => [[5],[]]
 => ([],1)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,2,3,5,4] => [4,1] => [[4,4],[3]]
 => ([],1)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,2,4,3,5] => [3,2] => [[4,3],[2]]
 => ([(0,1)],2)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,2,4,5,3] => [4,1] => [[4,4],[3]]
 => ([],1)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,2,5,3,4] => [3,2] => [[4,3],[2]]
 => ([(0,1)],2)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,2,5,4,3] => [3,1,1] => [[3,3,3],[2,2]]
 => ([],1)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,3,2,4,5] => [2,3] => [[4,2],[1]]
 => ([(0,1)],2)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,3,2,5,4] => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => 1
[1,3,4,2,5] => [3,2] => [[4,3],[2]]
 => ([(0,1)],2)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,3,4,5,2] => [4,1] => [[4,4],[3]]
 => ([],1)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,3,5,2,4] => [3,2] => [[4,3],[2]]
 => ([(0,1)],2)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,3,5,4,2] => [3,1,1] => [[3,3,3],[2,2]]
 => ([],1)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,4,2,3,5] => [2,3] => [[4,2],[1]]
 => ([(0,1)],2)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,4,2,5,3] => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => 1
[1,4,3,2,5] => [2,1,2] => [[3,2,2],[1,1]]
 => ([(0,1)],2)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,4,3,5,2] => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => 1
[1,4,5,2,3] => [3,2] => [[4,3],[2]]
 => ([(0,1)],2)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,4,5,3,2] => [3,1,1] => [[3,3,3],[2,2]]
 => ([],1)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,5,2,3,4] => [2,3] => [[4,2],[1]]
 => ([(0,1)],2)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,5,2,4,3] => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => 1
[1,5,3,2,4] => [2,1,2] => [[3,2,2],[1,1]]
 => ([(0,1)],2)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,5,3,4,2] => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => 1
[2,1,4,3,5] => [1,2,2] => [[3,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 1
[2,1,5,3,4] => [1,2,2] => [[3,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 1
[2,3,1,5,4] => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => 1
[2,4,1,5,3] => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => 1
[2,4,3,5,1] => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => 1
[2,5,1,4,3] => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => 1
[2,5,3,4,1] => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => 1
[3,1,4,2,5] => [1,2,2] => [[3,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 1
[3,1,5,2,4] => [1,2,2] => [[3,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 1
[3,2,4,1,5] => [1,2,2] => [[3,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 1
[3,2,5,1,4] => [1,2,2] => [[3,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 1
[3,4,1,5,2] => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => 1
[3,4,2,5,1] => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => 1
[3,5,1,4,2] => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => 1
[3,5,2,4,1] => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => 1
[4,1,3,2,5] => [1,2,2] => [[3,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 1
[4,1,5,2,3] => [1,2,2] => [[3,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 1
[4,2,3,1,5] => [1,2,2] => [[3,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 1
[4,2,5,1,3] => [1,2,2] => [[3,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 1
[4,3,5,1,2] => [1,2,2] => [[3,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 1
[4,5,1,3,2] => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => 1
[4,5,2,3,1] => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => 1
[5,1,3,2,4] => [1,2,2] => [[3,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 1
[5,1,4,2,3] => [1,2,2] => [[3,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 1
[5,2,3,1,4] => [1,2,2] => [[3,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 1
[5,2,4,1,3] => [1,2,2] => [[3,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 1
[5,3,4,1,2] => [1,2,2] => [[3,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 1
[1,2,4,3,5,6] => [3,3] => [[5,3],[2]]
 => ([(0,2),(2,1)],3)
 => 1
[1,2,4,3,6,5] => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,2),(2,1)],3)
 => 1
[1,2,5,3,4,6] => [3,3] => [[5,3],[2]]
 => ([(0,2),(2,1)],3)
 => 1
[1,2,5,3,6,4] => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,2),(2,1)],3)
 => 1
[1,2,5,4,6,3] => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,2),(2,1)],3)
 => 1
[1,2,6,3,4,5] => [3,3] => [[5,3],[2]]
 => ([(0,2),(2,1)],3)
 => 1
[1,2,6,3,5,4] => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,2),(2,1)],3)
 => 1
[1,2,6,4,5,3] => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,2),(2,1)],3)
 => 1
[1,3,2,4,6,5] => [2,3,1] => [[4,4,2],[3,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
[1,3,2,5,4,6] => [2,2,2] => [[4,3,2],[2,1]]
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 2
[1,3,2,5,6,4] => [2,3,1] => [[4,4,2],[3,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
[1,3,2,6,4,5] => [2,2,2] => [[4,3,2],[2,1]]
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 2
[1,3,2,6,5,4] => [2,2,1,1] => [[3,3,3,2],[2,2,1]]
 => ([(0,2),(2,1)],3)
 => 1
[1,3,4,2,5,6] => [3,3] => [[5,3],[2]]
 => ([(0,2),(2,1)],3)
 => 1
[1,3,4,2,6,5] => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,2),(2,1)],3)
 => 1
[1,3,5,2,4,6] => [3,3] => [[5,3],[2]]
 => ([(0,2),(2,1)],3)
 => 1
[1,3,5,2,6,4] => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,2),(2,1)],3)
 => 1
[1,3,5,4,6,2] => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,2),(2,1)],3)
 => 1

Description

The global dimension of the incidence algebra of the lattice over the rational numbers.

Matching statistic: St001878
(load all 7 compositions to match this statistic)

Mapping

Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00180: Integer compositions —to ribbon⟶ Skew partitions
Mp00192: Skew partitions —dominating sublattice⟶ Lattices
St001878: Lattices ⟶ ℤResult quality: 56% ●values known / values provided: 56%●distinct values known / distinct values provided: 67%

Values

[1] => [1] => [[1],[]]
 => ([],1)
 => ? = 0
[1,2] => [2] => [[2],[]]
 => ([],1)
 => ? ∊ {0,0}
[2,1] => [1,1] => [[1,1],[]]
 => ([],1)
 => ? ∊ {0,0}
[1,2,3] => [3] => [[3],[]]
 => ([],1)
 => ? ∊ {0,0,1,1,1,1}
[1,3,2] => [2,1] => [[2,2],[1]]
 => ([],1)
 => ? ∊ {0,0,1,1,1,1}
[2,1,3] => [1,2] => [[2,1],[]]
 => ([],1)
 => ? ∊ {0,0,1,1,1,1}
[2,3,1] => [2,1] => [[2,2],[1]]
 => ([],1)
 => ? ∊ {0,0,1,1,1,1}
[3,1,2] => [1,2] => [[2,1],[]]
 => ([],1)
 => ? ∊ {0,0,1,1,1,1}
[3,2,1] => [1,1,1] => [[1,1,1],[]]
 => ([],1)
 => ? ∊ {0,0,1,1,1,1}
[1,2,3,4] => [4] => [[4],[]]
 => ([],1)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[1,2,4,3] => [3,1] => [[3,3],[2]]
 => ([],1)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[1,3,2,4] => [2,2] => [[3,2],[1]]
 => ([(0,1)],2)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[1,3,4,2] => [3,1] => [[3,3],[2]]
 => ([],1)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[1,4,2,3] => [2,2] => [[3,2],[1]]
 => ([(0,1)],2)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[1,4,3,2] => [2,1,1] => [[2,2,2],[1,1]]
 => ([],1)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[2,1,3,4] => [1,3] => [[3,1],[]]
 => ([],1)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[2,1,4,3] => [1,2,1] => [[2,2,1],[1]]
 => ([(0,1)],2)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[2,3,1,4] => [2,2] => [[3,2],[1]]
 => ([(0,1)],2)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[2,3,4,1] => [3,1] => [[3,3],[2]]
 => ([],1)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[2,4,1,3] => [2,2] => [[3,2],[1]]
 => ([(0,1)],2)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[2,4,3,1] => [2,1,1] => [[2,2,2],[1,1]]
 => ([],1)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[3,1,2,4] => [1,3] => [[3,1],[]]
 => ([],1)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[3,1,4,2] => [1,2,1] => [[2,2,1],[1]]
 => ([(0,1)],2)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[3,2,1,4] => [1,1,2] => [[2,1,1],[]]
 => ([],1)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[3,2,4,1] => [1,2,1] => [[2,2,1],[1]]
 => ([(0,1)],2)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[3,4,1,2] => [2,2] => [[3,2],[1]]
 => ([(0,1)],2)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[3,4,2,1] => [2,1,1] => [[2,2,2],[1,1]]
 => ([],1)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[4,1,2,3] => [1,3] => [[3,1],[]]
 => ([],1)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[4,1,3,2] => [1,2,1] => [[2,2,1],[1]]
 => ([(0,1)],2)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[4,2,1,3] => [1,1,2] => [[2,1,1],[]]
 => ([],1)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[4,2,3,1] => [1,2,1] => [[2,2,1],[1]]
 => ([(0,1)],2)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[4,3,1,2] => [1,1,2] => [[2,1,1],[]]
 => ([],1)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[4,3,2,1] => [1,1,1,1] => [[1,1,1,1],[]]
 => ([],1)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[1,2,3,4,5] => [5] => [[5],[]]
 => ([],1)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,2,3,5,4] => [4,1] => [[4,4],[3]]
 => ([],1)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,2,4,3,5] => [3,2] => [[4,3],[2]]
 => ([(0,1)],2)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,2,4,5,3] => [4,1] => [[4,4],[3]]
 => ([],1)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,2,5,3,4] => [3,2] => [[4,3],[2]]
 => ([(0,1)],2)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,2,5,4,3] => [3,1,1] => [[3,3,3],[2,2]]
 => ([],1)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,3,2,4,5] => [2,3] => [[4,2],[1]]
 => ([(0,1)],2)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,3,2,5,4] => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => 1
[1,3,4,2,5] => [3,2] => [[4,3],[2]]
 => ([(0,1)],2)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,3,4,5,2] => [4,1] => [[4,4],[3]]
 => ([],1)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,3,5,2,4] => [3,2] => [[4,3],[2]]
 => ([(0,1)],2)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,3,5,4,2] => [3,1,1] => [[3,3,3],[2,2]]
 => ([],1)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,4,2,3,5] => [2,3] => [[4,2],[1]]
 => ([(0,1)],2)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,4,2,5,3] => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => 1
[1,4,3,2,5] => [2,1,2] => [[3,2,2],[1,1]]
 => ([(0,1)],2)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,4,3,5,2] => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => 1
[1,4,5,2,3] => [3,2] => [[4,3],[2]]
 => ([(0,1)],2)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,4,5,3,2] => [3,1,1] => [[3,3,3],[2,2]]
 => ([],1)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,5,2,3,4] => [2,3] => [[4,2],[1]]
 => ([(0,1)],2)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,5,2,4,3] => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => 1
[1,5,3,2,4] => [2,1,2] => [[3,2,2],[1,1]]
 => ([(0,1)],2)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,5,3,4,2] => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => 1
[2,1,4,3,5] => [1,2,2] => [[3,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 1
[2,1,5,3,4] => [1,2,2] => [[3,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 1
[2,3,1,5,4] => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => 1
[2,4,1,5,3] => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => 1
[2,4,3,5,1] => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => 1
[2,5,1,4,3] => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => 1
[2,5,3,4,1] => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => 1
[3,1,4,2,5] => [1,2,2] => [[3,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 1
[3,1,5,2,4] => [1,2,2] => [[3,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 1
[3,2,4,1,5] => [1,2,2] => [[3,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 1
[3,2,5,1,4] => [1,2,2] => [[3,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 1
[3,4,1,5,2] => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => 1
[3,4,2,5,1] => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => 1
[3,5,1,4,2] => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => 1
[3,5,2,4,1] => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => 1
[4,1,3,2,5] => [1,2,2] => [[3,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 1
[4,1,5,2,3] => [1,2,2] => [[3,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 1
[4,2,3,1,5] => [1,2,2] => [[3,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 1
[4,2,5,1,3] => [1,2,2] => [[3,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 1
[4,3,5,1,2] => [1,2,2] => [[3,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 1
[4,5,1,3,2] => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => 1
[4,5,2,3,1] => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => 1
[5,1,3,2,4] => [1,2,2] => [[3,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 1
[5,1,4,2,3] => [1,2,2] => [[3,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 1
[5,2,3,1,4] => [1,2,2] => [[3,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 1
[5,2,4,1,3] => [1,2,2] => [[3,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 1
[5,3,4,1,2] => [1,2,2] => [[3,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 1
[1,2,4,3,5,6] => [3,3] => [[5,3],[2]]
 => ([(0,2),(2,1)],3)
 => 1
[1,2,4,3,6,5] => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,2),(2,1)],3)
 => 1
[1,2,5,3,4,6] => [3,3] => [[5,3],[2]]
 => ([(0,2),(2,1)],3)
 => 1
[1,2,5,3,6,4] => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,2),(2,1)],3)
 => 1
[1,2,5,4,6,3] => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,2),(2,1)],3)
 => 1
[1,2,6,3,4,5] => [3,3] => [[5,3],[2]]
 => ([(0,2),(2,1)],3)
 => 1
[1,2,6,3,5,4] => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,2),(2,1)],3)
 => 1
[1,2,6,4,5,3] => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,2),(2,1)],3)
 => 1
[1,3,2,4,6,5] => [2,3,1] => [[4,4,2],[3,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
[1,3,2,5,4,6] => [2,2,2] => [[4,3,2],[2,1]]
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 2
[1,3,2,5,6,4] => [2,3,1] => [[4,4,2],[3,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
[1,3,2,6,4,5] => [2,2,2] => [[4,3,2],[2,1]]
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 2
[1,3,2,6,5,4] => [2,2,1,1] => [[3,3,3,2],[2,2,1]]
 => ([(0,2),(2,1)],3)
 => 1
[1,3,4,2,5,6] => [3,3] => [[5,3],[2]]
 => ([(0,2),(2,1)],3)
 => 1
[1,3,4,2,6,5] => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,2),(2,1)],3)
 => 1
[1,3,5,2,4,6] => [3,3] => [[5,3],[2]]
 => ([(0,2),(2,1)],3)
 => 1
[1,3,5,2,6,4] => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,2),(2,1)],3)
 => 1
[1,3,5,4,6,2] => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,2),(2,1)],3)
 => 1

Description

The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L.

Matching statistic: St000937

Mapping

Mp00223: Permutations —runsort⟶ Permutations
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000937: Integer partitions ⟶ ℤResult quality: 48% ●values known / values provided: 48%●distinct values known / distinct values provided: 67%

Values

[1] => [1] => [1]
 => []
 => ? = 0
[1,2] => [1,2] => [2]
 => []
 => ? ∊ {0,0}
[2,1] => [1,2] => [2]
 => []
 => ? ∊ {0,0}
[1,2,3] => [1,2,3] => [3]
 => []
 => ? ∊ {0,0,1,1,1,1}
[1,3,2] => [1,3,2] => [2,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1}
[2,1,3] => [1,3,2] => [2,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1}
[2,3,1] => [1,2,3] => [3]
 => []
 => ? ∊ {0,0,1,1,1,1}
[3,1,2] => [1,2,3] => [3]
 => []
 => ? ∊ {0,0,1,1,1,1}
[3,2,1] => [1,2,3] => [3]
 => []
 => ? ∊ {0,0,1,1,1,1}
[1,2,3,4] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[1,2,4,3] => [1,2,4,3] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[1,3,2,4] => [1,3,2,4] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[1,3,4,2] => [1,3,4,2] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[1,4,2,3] => [1,4,2,3] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[1,4,3,2] => [1,4,2,3] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[2,1,3,4] => [1,3,4,2] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[2,1,4,3] => [1,4,2,3] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[2,3,1,4] => [1,4,2,3] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[2,3,4,1] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[2,4,1,3] => [1,3,2,4] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[2,4,3,1] => [1,2,4,3] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[3,1,2,4] => [1,2,4,3] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[3,1,4,2] => [1,4,2,3] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[3,2,1,4] => [1,4,2,3] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[3,2,4,1] => [1,2,4,3] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[3,4,1,2] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[3,4,2,1] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[4,1,2,3] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[4,1,3,2] => [1,3,2,4] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[4,2,1,3] => [1,3,2,4] => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[4,2,3,1] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[4,3,1,2] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[4,3,2,1] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[1,2,3,4,5] => [1,2,3,4,5] => [5]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,2,3,5,4] => [1,2,3,5,4] => [4,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,2,4,3,5] => [1,2,4,3,5] => [4,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,2,4,5,3] => [1,2,4,5,3] => [4,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,2,5,3,4] => [1,2,5,3,4] => [4,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,2,5,4,3] => [1,2,5,3,4] => [4,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,3,2,4,5] => [1,3,2,4,5] => [4,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,3,2,5,4] => [1,3,2,5,4] => [3,2]
 => [2]
 => 2
[1,3,4,2,5] => [1,3,4,2,5] => [4,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,3,4,5,2] => [1,3,4,5,2] => [4,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,3,5,2,4] => [1,3,5,2,4] => [3,2]
 => [2]
 => 2
[1,3,5,4,2] => [1,3,5,2,4] => [3,2]
 => [2]
 => 2
[1,4,2,3,5] => [1,4,2,3,5] => [4,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,4,2,5,3] => [1,4,2,5,3] => [3,2]
 => [2]
 => 2
[1,4,3,2,5] => [1,4,2,5,3] => [3,2]
 => [2]
 => 2
[1,4,3,5,2] => [1,4,2,3,5] => [4,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,4,5,2,3] => [1,4,5,2,3] => [3,2]
 => [2]
 => 2
[1,4,5,3,2] => [1,4,5,2,3] => [3,2]
 => [2]
 => 2
[1,5,2,3,4] => [1,5,2,3,4] => [4,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,5,2,4,3] => [1,5,2,4,3] => [3,1,1]
 => [1,1]
 => 1
[1,5,3,2,4] => [1,5,2,4,3] => [3,1,1]
 => [1,1]
 => 1
[1,5,3,4,2] => [1,5,2,3,4] => [4,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,5,4,2,3] => [1,5,2,3,4] => [4,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[1,5,4,3,2] => [1,5,2,3,4] => [4,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,1,3,4,5] => [1,3,4,5,2] => [4,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,1,3,5,4] => [1,3,5,2,4] => [3,2]
 => [2]
 => 2
[2,1,4,3,5] => [1,4,2,3,5] => [4,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
[2,1,4,5,3] => [1,4,5,2,3] => [3,2]
 => [2]
 => 2
[2,3,1,4,5] => [1,4,5,2,3] => [3,2]
 => [2]
 => 2
[2,4,1,3,5] => [1,3,5,2,4] => [3,2]
 => [2]
 => 2
[2,4,1,5,3] => [1,5,2,4,3] => [3,1,1]
 => [1,1]
 => 1
[2,4,3,1,5] => [1,5,2,4,3] => [3,1,1]
 => [1,1]
 => 1
[2,5,1,4,3] => [1,4,2,5,3] => [3,2]
 => [2]
 => 2
[2,5,3,1,4] => [1,4,2,5,3] => [3,2]
 => [2]
 => 2
[2,5,4,1,3] => [1,3,2,5,4] => [3,2]
 => [2]
 => 2
[3,1,4,2,5] => [1,4,2,5,3] => [3,2]
 => [2]
 => 2
[3,1,4,5,2] => [1,4,5,2,3] => [3,2]
 => [2]
 => 2
[3,1,5,2,4] => [1,5,2,4,3] => [3,1,1]
 => [1,1]
 => 1
[3,2,1,4,5] => [1,4,5,2,3] => [3,2]
 => [2]
 => 2
[3,2,4,1,5] => [1,5,2,4,3] => [3,1,1]
 => [1,1]
 => 1
[3,2,5,1,4] => [1,4,2,5,3] => [3,2]
 => [2]
 => 2
[4,1,3,2,5] => [1,3,2,5,4] => [3,2]
 => [2]
 => 2
[4,1,3,5,2] => [1,3,5,2,4] => [3,2]
 => [2]
 => 2
[4,2,1,3,5] => [1,3,5,2,4] => [3,2]
 => [2]
 => 2
[4,2,5,1,3] => [1,3,2,5,4] => [3,2]
 => [2]
 => 2
[1,2,4,3,6,5] => [1,2,4,3,6,5] => [4,2]
 => [2]
 => 2
[1,2,4,6,3,5] => [1,2,4,6,3,5] => [4,2]
 => [2]
 => 2
[1,2,4,6,5,3] => [1,2,4,6,3,5] => [4,2]
 => [2]
 => 2
[1,2,5,3,6,4] => [1,2,5,3,6,4] => [4,2]
 => [2]
 => 2
[1,2,5,4,3,6] => [1,2,5,3,6,4] => [4,2]
 => [2]
 => 2
[1,2,5,6,3,4] => [1,2,5,6,3,4] => [4,2]
 => [2]
 => 2
[1,2,5,6,4,3] => [1,2,5,6,3,4] => [4,2]
 => [2]
 => 2
[1,2,6,3,5,4] => [1,2,6,3,5,4] => [4,1,1]
 => [1,1]
 => 1
[1,2,6,4,3,5] => [1,2,6,3,5,4] => [4,1,1]
 => [1,1]
 => 1
[1,3,2,4,6,5] => [1,3,2,4,6,5] => [4,2]
 => [2]
 => 2
[1,3,2,5,4,6] => [1,3,2,5,4,6] => [4,2]
 => [2]
 => 2
[1,3,2,5,6,4] => [1,3,2,5,6,4] => [4,2]
 => [2]
 => 2
[1,3,2,6,4,5] => [1,3,2,6,4,5] => [4,2]
 => [2]
 => 2
[1,3,2,6,5,4] => [1,3,2,6,4,5] => [4,2]
 => [2]
 => 2
[1,3,4,2,6,5] => [1,3,4,2,6,5] => [4,2]
 => [2]
 => 2
[1,3,4,6,2,5] => [1,3,4,6,2,5] => [4,2]
 => [2]
 => 2
[1,3,4,6,5,2] => [1,3,4,6,2,5] => [4,2]
 => [2]
 => 2
[1,3,5,2,4,6] => [1,3,5,2,4,6] => [4,2]
 => [2]
 => 2
[1,3,5,2,6,4] => [1,3,5,2,6,4] => [4,2]
 => [2]
 => 2
[1,3,5,4,2,6] => [1,3,5,2,6,4] => [4,2]
 => [2]
 => 2
[1,3,5,4,6,2] => [1,3,5,2,4,6] => [4,2]
 => [2]
 => 2
[1,3,5,6,2,4] => [1,3,5,6,2,4] => [4,2]
 => [2]
 => 2

Description

The number of positive values of the symmetric group character corresponding to the partition. For example, the character values of the irreducible representation

$S^{(2,2)}$ are

$2$ on the conjugacy classes

$(4)$ and

$(2,2)$ ,

$0$ on the conjugacy classes

$(3,1)$ and

$(1,1,1,1)$ , and

$-1$ on the conjugacy class

$(2,1,1)$ . Therefore, the statistic on the partition

$(2,2)$ is

$2$ .

The following 51 statistics, ordered by result quality, also match your data. Click on any of them to see the details.

St001603The number of colourings of a polygon such that the multiplicities of a colour are given by a partition. St001604The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on polygons. St001605The number of colourings of a cycle such that the multiplicities of colours are given by a partition. St001877Number of indecomposable injective modules with projective dimension 2. St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset. St000456The monochromatic index of a connected graph. St000284The Plancherel distribution on integer partitions. St000698The number of 2-rim hooks removed from an integer partition to obtain its associated 2-core. St000704The number of semistandard tableaux on a given integer partition with minimal maximal entry. 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. St000901The cube of the number of standard Young tableaux with shape given by the partition. St001128The exponens consonantiae of a partition. St001712The number of natural descents of a standard Young tableau. St001200The number of simple modules in

$eAe$ with projective dimension at most 2 in the corresponding Nakayama algebra

$A$ with minimal faithful projective-injective module

$eA$ . St000455The second largest eigenvalue of a graph if it is integral. St001575The minimal number of edges to add or remove to make a graph edge transitive. St001577The minimal number of edges to add or remove to make a graph a cograph. St001960The number of descents of a permutation minus one if its first entry is not one. St000632The jump number of the poset. St000298The order dimension or Dushnik-Miller dimension of a poset. St000257The number of distinct parts of a partition that occur at least twice. St000143The largest repeated part of a partition. St000527The width of the poset. St001568The smallest positive integer that does not appear twice in the partition. St000454The largest eigenvalue of a graph if it is integral. St001335The cardinality of a minimal cycle-isolating set of a graph. St000640The rank of the largest boolean interval in a 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. St000535The rank-width of a graph. St000671The maximin edge-connectivity for choosing a subgraph. St001743The discrepancy of a graph. St001826The maximal number of leaves on a vertex of a graph. St000273The domination number of a graph. St000544The cop number of a graph. St001322The size of a minimal independent dominating set in a graph. St001339The irredundance number of a graph. St000771The largest multiplicity of a distance Laplacian eigenvalue in a connected graph. St000785The number of distinct colouring schemes of a graph. St001029The size of the core of a graph. St001494The Alon-Tarsi number of a graph. St001829The common independence number of a graph. St001569The maximal modular displacement of a permutation. St001582The grades of the simple modules corresponding to the points in the poset of the symmetric group under the Bruhat order. St000307The number of rowmotion orbits of a poset. St000822The Hadwiger number of the graph. St001330The hat guessing number of a graph. St001642The Prague dimension of a graph. St001271The competition number of a graph.