Your data matches 28 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001271
Mapping
Mp00156: Graphs —line graph⟶ Graphs
Mp00111: Graphs —complement⟶ Graphs
Mp00117: Graphs —Ore closure⟶ Graphs
St001271: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([(0,1)],2)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(1,2)],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ([],2)
 => 0
([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ([],3)
 => 0
([(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ([],2)
 => 0
([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ([],3)
 => 0
([(0,3),(1,2)],4)
 => ([],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 1
([(0,3),(1,2),(2,3)],4)
 => ([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => ([(1,2)],3)
 => 0
([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ([],3)
 => 0
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ([(2,3)],4)
 => 0
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,3)],5)
 => ([(1,4),(2,3)],5)
 => 0
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,5),(1,4),(2,3)],6)
 => ([(0,5),(1,4),(2,3)],6)
 => 1
([(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ([],2)
 => 0
([(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ([],3)
 => 0
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ([],4)
 => 0
([(1,4),(2,3)],5)
 => ([],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 1
([(1,4),(2,3),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => ([(1,2)],3)
 => 0
([(0,1),(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 1
([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ([],3)
 => 0
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => 0
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ([(2,3)],4)
 => 0
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => 0
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,3)],5)
 => ([(1,4),(2,3)],5)
 => 0
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => 0
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 0
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => 2
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6),(5,6)],7)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6),(5,6)],7)
 => 2
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,5),(1,4),(2,3)],6)
 => ([(0,5),(1,4),(2,3)],6)
 => 1
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(5,6)],7)
 => ([(0,3),(0,6),(1,2),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => ([(0,3),(0,6),(1,2),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => 3
([(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ([],2)
 => 0
([(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ([],3)
 => 0
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ([],4)
 => 0
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ([],5)
 => 0
([(2,5),(3,4)],6)
 => ([],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 1
([(2,5),(3,4),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => ([(1,2)],3)
 => 0
([(1,2),(3,5),(4,5)],6)
 => ([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 1
Description
The competition number of a graph. The competition graph of a digraph $D$ is a (simple undirected) graph which has the same vertex set as $D$ and has an edge between $x$ and $y$ if and only if there exists a vertex $v$ in $D$ such that $(x, v)$ and $(y, v)$ are arcs of $D$. For any graph, $G$ together with sufficiently many isolated vertices is the competition graph of some acyclic digraph. The competition number $k(G)$ is the smallest number of such isolated vertices.
Matching statistic: St000618
(load all 2 compositions to match this statistic)
Mapping
Mp00275: Graphs —to edge-partition of connected components⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000618: Integer partitions ⟶ ℤResult quality: 20% ●values known / values provided: 21%●distinct values known / distinct values provided: 20%
Values
([(0,1)],2)
 => [1]
 => []
 => ? = 0
([(1,2)],3)
 => [1]
 => []
 => ? = 0
([(0,2),(1,2)],3)
 => [2]
 => []
 => ? = 0
([(0,1),(0,2),(1,2)],3)
 => [3]
 => []
 => ? = 0
([(2,3)],4)
 => [1]
 => []
 => ? = 0
([(1,3),(2,3)],4)
 => [2]
 => []
 => ? = 0
([(0,3),(1,3),(2,3)],4)
 => [3]
 => []
 => ? = 0
([(0,3),(1,2)],4)
 => [1,1]
 => [1]
 => 1
([(0,3),(1,2),(2,3)],4)
 => [3]
 => []
 => ? = 0
([(1,2),(1,3),(2,3)],4)
 => [3]
 => []
 => ? = 0
([(0,3),(1,2),(1,3),(2,3)],4)
 => [4]
 => []
 => ? = 0
([(0,2),(0,3),(1,2),(1,3)],4)
 => [4]
 => []
 => ? = 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [5]
 => []
 => ? = 0
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [6]
 => []
 => ? = 1
([(3,4)],5)
 => [1]
 => []
 => ? = 0
([(2,4),(3,4)],5)
 => [2]
 => []
 => ? = 0
([(1,4),(2,4),(3,4)],5)
 => [3]
 => []
 => ? = 0
([(0,4),(1,4),(2,4),(3,4)],5)
 => [4]
 => []
 => ? = 0
([(1,4),(2,3)],5)
 => [1,1]
 => [1]
 => 1
([(1,4),(2,3),(3,4)],5)
 => [3]
 => []
 => ? = 0
([(0,1),(2,4),(3,4)],5)
 => [2,1]
 => [1]
 => 1
([(2,3),(2,4),(3,4)],5)
 => [3]
 => []
 => ? = 0
([(0,4),(1,4),(2,3),(3,4)],5)
 => [4]
 => []
 => ? = 0
([(1,4),(2,3),(2,4),(3,4)],5)
 => [4]
 => []
 => ? = 0
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 0
([(1,3),(1,4),(2,3),(2,4)],5)
 => [4]
 => []
 => ? = 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 0
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 0
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [6]
 => []
 => ? = 0
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [6]
 => []
 => ? = 2
([(0,4),(1,3),(2,3),(2,4)],5)
 => [4]
 => []
 => ? = 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => [3,1]
 => [1]
 => 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => [6]
 => []
 => ? = 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => [5]
 => []
 => ? = 2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [6]
 => []
 => ? = 2
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => [7]
 => []
 => ? = 2
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => [6]
 => []
 => ? = 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [6]
 => []
 => ? = 1
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [7]
 => []
 => ? = 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => [7]
 => []
 => ? = 3
([(4,5)],6)
 => [1]
 => []
 => ? = 0
([(3,5),(4,5)],6)
 => [2]
 => []
 => ? = 0
([(2,5),(3,5),(4,5)],6)
 => [3]
 => []
 => ? = 0
([(1,5),(2,5),(3,5),(4,5)],6)
 => [4]
 => []
 => ? = 0
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => [5]
 => []
 => ? = 0
([(2,5),(3,4)],6)
 => [1,1]
 => [1]
 => 1
([(2,5),(3,4),(4,5)],6)
 => [3]
 => []
 => ? = 0
([(1,2),(3,5),(4,5)],6)
 => [2,1]
 => [1]
 => 1
([(3,4),(3,5),(4,5)],6)
 => [3]
 => []
 => ? = 0
([(1,5),(2,5),(3,4),(4,5)],6)
 => [4]
 => []
 => ? = 0
([(0,1),(2,5),(3,5),(4,5)],6)
 => [3,1]
 => [1]
 => 1
([(2,5),(3,4),(3,5),(4,5)],6)
 => [4]
 => []
 => ? = 0
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => [5]
 => []
 => ? = 0
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => [5]
 => []
 => ? = 0
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 0
([(0,5),(1,5),(2,4),(3,4)],6)
 => [2,2]
 => [2]
 => 1
([(0,5),(1,4),(2,3)],6)
 => [1,1,1]
 => [1,1]
 => 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => [3,1]
 => [1]
 => 1
([(1,2),(3,4),(3,5),(4,5)],6)
 => [3,1]
 => [1]
 => 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1]
 => [1]
 => 1
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => [4,1]
 => [1]
 => 1
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => [3,2]
 => [2]
 => 1
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => [3,3]
 => [3]
 => 1
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6,1]
 => [1]
 => 1
([(3,6),(4,5)],7)
 => [1,1]
 => [1]
 => 1
([(2,3),(4,6),(5,6)],7)
 => [2,1]
 => [1]
 => 1
([(1,2),(3,6),(4,6),(5,6)],7)
 => [3,1]
 => [1]
 => 1
([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
 => [4,1]
 => [1]
 => 1
([(1,6),(2,6),(3,5),(4,5)],7)
 => [2,2]
 => [2]
 => 1
([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
 => [3,2]
 => [2]
 => 1
([(1,6),(2,5),(3,4)],7)
 => [1,1,1]
 => [1,1]
 => 1
([(1,2),(3,6),(4,5),(5,6)],7)
 => [3,1]
 => [1]
 => 1
([(0,3),(1,2),(4,6),(5,6)],7)
 => [2,1,1]
 => [1,1]
 => 1
([(2,3),(4,5),(4,6),(5,6)],7)
 => [3,1]
 => [1]
 => 1
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
 => [4,1]
 => [1]
 => 1
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
 => [4,1]
 => [1]
 => 1
([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1]
 => 1
([(1,2),(3,5),(3,6),(4,5),(4,6)],7)
 => [4,1]
 => [1]
 => 1
([(0,6),(1,5),(2,4),(3,4),(5,6)],7)
 => [3,2]
 => [2]
 => 1
([(1,6),(2,6),(3,4),(3,5),(4,5)],7)
 => [3,2]
 => [2]
 => 1
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => [5,1]
 => [1]
 => 1
([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
 => [4,2]
 => [2]
 => 1
([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1]
 => 1
([(0,1),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1]
 => 1
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7)
 => [3,3]
 => [3]
 => 1
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7)
 => [4,2]
 => [2]
 => 1
([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7)
 => [5,2]
 => [2]
 => 1
([(0,1),(2,5),(3,4),(4,6),(5,6)],7)
 => [4,1]
 => [1]
 => 1
([(0,3),(1,2),(4,5),(4,6),(5,6)],7)
 => [3,1,1]
 => [1,1]
 => 1
([(0,1),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1]
 => 1
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5)],7)
 => [5,1]
 => [1]
 => 1
([(0,6),(1,5),(2,3),(2,4),(3,4),(5,6)],7)
 => [3,3]
 => [3]
 => 1
([(0,1),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1
([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7)
 => [3,3]
 => [3]
 => 1
([(0,1),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1
Description
The number of self-evacuating tableaux of given shape. This is the same as the number of standard domino tableaux of the given shape.
Matching statistic: St000781
(load all 2 compositions to match this statistic)
Mapping
Mp00275: Graphs —to edge-partition of connected components⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000781: Integer partitions ⟶ ℤResult quality: 20% ●values known / values provided: 21%●distinct values known / distinct values provided: 20%
Values
([(0,1)],2)
 => [1]
 => []
 => ? = 0
([(1,2)],3)
 => [1]
 => []
 => ? = 0
([(0,2),(1,2)],3)
 => [2]
 => []
 => ? = 0
([(0,1),(0,2),(1,2)],3)
 => [3]
 => []
 => ? = 0
([(2,3)],4)
 => [1]
 => []
 => ? = 0
([(1,3),(2,3)],4)
 => [2]
 => []
 => ? = 0
([(0,3),(1,3),(2,3)],4)
 => [3]
 => []
 => ? = 0
([(0,3),(1,2)],4)
 => [1,1]
 => [1]
 => 1
([(0,3),(1,2),(2,3)],4)
 => [3]
 => []
 => ? = 0
([(1,2),(1,3),(2,3)],4)
 => [3]
 => []
 => ? = 0
([(0,3),(1,2),(1,3),(2,3)],4)
 => [4]
 => []
 => ? = 0
([(0,2),(0,3),(1,2),(1,3)],4)
 => [4]
 => []
 => ? = 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [5]
 => []
 => ? = 0
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [6]
 => []
 => ? = 1
([(3,4)],5)
 => [1]
 => []
 => ? = 0
([(2,4),(3,4)],5)
 => [2]
 => []
 => ? = 0
([(1,4),(2,4),(3,4)],5)
 => [3]
 => []
 => ? = 0
([(0,4),(1,4),(2,4),(3,4)],5)
 => [4]
 => []
 => ? = 0
([(1,4),(2,3)],5)
 => [1,1]
 => [1]
 => 1
([(1,4),(2,3),(3,4)],5)
 => [3]
 => []
 => ? = 0
([(0,1),(2,4),(3,4)],5)
 => [2,1]
 => [1]
 => 1
([(2,3),(2,4),(3,4)],5)
 => [3]
 => []
 => ? = 0
([(0,4),(1,4),(2,3),(3,4)],5)
 => [4]
 => []
 => ? = 0
([(1,4),(2,3),(2,4),(3,4)],5)
 => [4]
 => []
 => ? = 0
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 0
([(1,3),(1,4),(2,3),(2,4)],5)
 => [4]
 => []
 => ? = 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 0
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 0
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [6]
 => []
 => ? = 0
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [6]
 => []
 => ? = 2
([(0,4),(1,3),(2,3),(2,4)],5)
 => [4]
 => []
 => ? = 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => [3,1]
 => [1]
 => 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => [6]
 => []
 => ? = 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => [5]
 => []
 => ? = 2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [6]
 => []
 => ? = 2
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => [7]
 => []
 => ? = 2
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => [6]
 => []
 => ? = 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [6]
 => []
 => ? = 1
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [7]
 => []
 => ? = 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => [7]
 => []
 => ? = 3
([(4,5)],6)
 => [1]
 => []
 => ? = 0
([(3,5),(4,5)],6)
 => [2]
 => []
 => ? = 0
([(2,5),(3,5),(4,5)],6)
 => [3]
 => []
 => ? = 0
([(1,5),(2,5),(3,5),(4,5)],6)
 => [4]
 => []
 => ? = 0
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => [5]
 => []
 => ? = 0
([(2,5),(3,4)],6)
 => [1,1]
 => [1]
 => 1
([(2,5),(3,4),(4,5)],6)
 => [3]
 => []
 => ? = 0
([(1,2),(3,5),(4,5)],6)
 => [2,1]
 => [1]
 => 1
([(3,4),(3,5),(4,5)],6)
 => [3]
 => []
 => ? = 0
([(1,5),(2,5),(3,4),(4,5)],6)
 => [4]
 => []
 => ? = 0
([(0,1),(2,5),(3,5),(4,5)],6)
 => [3,1]
 => [1]
 => 1
([(2,5),(3,4),(3,5),(4,5)],6)
 => [4]
 => []
 => ? = 0
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => [5]
 => []
 => ? = 0
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => [5]
 => []
 => ? = 0
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 0
([(0,5),(1,5),(2,4),(3,4)],6)
 => [2,2]
 => [2]
 => 1
([(0,5),(1,4),(2,3)],6)
 => [1,1,1]
 => [1,1]
 => 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => [3,1]
 => [1]
 => 1
([(1,2),(3,4),(3,5),(4,5)],6)
 => [3,1]
 => [1]
 => 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1]
 => [1]
 => 1
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => [4,1]
 => [1]
 => 1
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => [3,2]
 => [2]
 => 1
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => [3,3]
 => [3]
 => 1
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6,1]
 => [1]
 => 1
([(3,6),(4,5)],7)
 => [1,1]
 => [1]
 => 1
([(2,3),(4,6),(5,6)],7)
 => [2,1]
 => [1]
 => 1
([(1,2),(3,6),(4,6),(5,6)],7)
 => [3,1]
 => [1]
 => 1
([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
 => [4,1]
 => [1]
 => 1
([(1,6),(2,6),(3,5),(4,5)],7)
 => [2,2]
 => [2]
 => 1
([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
 => [3,2]
 => [2]
 => 1
([(1,6),(2,5),(3,4)],7)
 => [1,1,1]
 => [1,1]
 => 1
([(1,2),(3,6),(4,5),(5,6)],7)
 => [3,1]
 => [1]
 => 1
([(0,3),(1,2),(4,6),(5,6)],7)
 => [2,1,1]
 => [1,1]
 => 1
([(2,3),(4,5),(4,6),(5,6)],7)
 => [3,1]
 => [1]
 => 1
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
 => [4,1]
 => [1]
 => 1
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
 => [4,1]
 => [1]
 => 1
([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1]
 => 1
([(1,2),(3,5),(3,6),(4,5),(4,6)],7)
 => [4,1]
 => [1]
 => 1
([(0,6),(1,5),(2,4),(3,4),(5,6)],7)
 => [3,2]
 => [2]
 => 1
([(1,6),(2,6),(3,4),(3,5),(4,5)],7)
 => [3,2]
 => [2]
 => 1
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => [5,1]
 => [1]
 => 1
([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
 => [4,2]
 => [2]
 => 1
([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1]
 => 1
([(0,1),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1]
 => 1
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7)
 => [3,3]
 => [3]
 => 1
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7)
 => [4,2]
 => [2]
 => 1
([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7)
 => [5,2]
 => [2]
 => 1
([(0,1),(2,5),(3,4),(4,6),(5,6)],7)
 => [4,1]
 => [1]
 => 1
([(0,3),(1,2),(4,5),(4,6),(5,6)],7)
 => [3,1,1]
 => [1,1]
 => 1
([(0,1),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1]
 => 1
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5)],7)
 => [5,1]
 => [1]
 => 1
([(0,6),(1,5),(2,3),(2,4),(3,4),(5,6)],7)
 => [3,3]
 => [3]
 => 1
([(0,1),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1
([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7)
 => [3,3]
 => [3]
 => 1
([(0,1),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1
Description
The number of proper colouring schemes of a Ferrers diagram. A colouring of a Ferrers diagram is proper if no two cells in a row or in a column have the same colour. The minimal number of colours needed is the maximum of the length and the first part of the partition, because we can restrict a latin square to the shape. We can associate to each colouring the integer partition recording how often each colour is used, see [1]. This statistic is the number of distinct such integer partitions that occur.
Matching statistic: St001432
(load all 2 compositions to match this statistic)
Mapping
Mp00275: Graphs —to edge-partition of connected components⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001432: Integer partitions ⟶ ℤResult quality: 20% ●values known / values provided: 21%●distinct values known / distinct values provided: 20%
Values
([(0,1)],2)
 => [1]
 => []
 => ? = 0
([(1,2)],3)
 => [1]
 => []
 => ? = 0
([(0,2),(1,2)],3)
 => [2]
 => []
 => ? = 0
([(0,1),(0,2),(1,2)],3)
 => [3]
 => []
 => ? = 0
([(2,3)],4)
 => [1]
 => []
 => ? = 0
([(1,3),(2,3)],4)
 => [2]
 => []
 => ? = 0
([(0,3),(1,3),(2,3)],4)
 => [3]
 => []
 => ? = 0
([(0,3),(1,2)],4)
 => [1,1]
 => [1]
 => 1
([(0,3),(1,2),(2,3)],4)
 => [3]
 => []
 => ? = 0
([(1,2),(1,3),(2,3)],4)
 => [3]
 => []
 => ? = 0
([(0,3),(1,2),(1,3),(2,3)],4)
 => [4]
 => []
 => ? = 0
([(0,2),(0,3),(1,2),(1,3)],4)
 => [4]
 => []
 => ? = 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [5]
 => []
 => ? = 0
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [6]
 => []
 => ? = 1
([(3,4)],5)
 => [1]
 => []
 => ? = 0
([(2,4),(3,4)],5)
 => [2]
 => []
 => ? = 0
([(1,4),(2,4),(3,4)],5)
 => [3]
 => []
 => ? = 0
([(0,4),(1,4),(2,4),(3,4)],5)
 => [4]
 => []
 => ? = 0
([(1,4),(2,3)],5)
 => [1,1]
 => [1]
 => 1
([(1,4),(2,3),(3,4)],5)
 => [3]
 => []
 => ? = 0
([(0,1),(2,4),(3,4)],5)
 => [2,1]
 => [1]
 => 1
([(2,3),(2,4),(3,4)],5)
 => [3]
 => []
 => ? = 0
([(0,4),(1,4),(2,3),(3,4)],5)
 => [4]
 => []
 => ? = 0
([(1,4),(2,3),(2,4),(3,4)],5)
 => [4]
 => []
 => ? = 0
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 0
([(1,3),(1,4),(2,3),(2,4)],5)
 => [4]
 => []
 => ? = 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 0
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 0
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [6]
 => []
 => ? = 0
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [6]
 => []
 => ? = 2
([(0,4),(1,3),(2,3),(2,4)],5)
 => [4]
 => []
 => ? = 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => [3,1]
 => [1]
 => 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => [6]
 => []
 => ? = 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => [5]
 => []
 => ? = 2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [6]
 => []
 => ? = 2
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => [7]
 => []
 => ? = 2
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => [6]
 => []
 => ? = 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [6]
 => []
 => ? = 1
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [7]
 => []
 => ? = 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => [7]
 => []
 => ? = 3
([(4,5)],6)
 => [1]
 => []
 => ? = 0
([(3,5),(4,5)],6)
 => [2]
 => []
 => ? = 0
([(2,5),(3,5),(4,5)],6)
 => [3]
 => []
 => ? = 0
([(1,5),(2,5),(3,5),(4,5)],6)
 => [4]
 => []
 => ? = 0
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => [5]
 => []
 => ? = 0
([(2,5),(3,4)],6)
 => [1,1]
 => [1]
 => 1
([(2,5),(3,4),(4,5)],6)
 => [3]
 => []
 => ? = 0
([(1,2),(3,5),(4,5)],6)
 => [2,1]
 => [1]
 => 1
([(3,4),(3,5),(4,5)],6)
 => [3]
 => []
 => ? = 0
([(1,5),(2,5),(3,4),(4,5)],6)
 => [4]
 => []
 => ? = 0
([(0,1),(2,5),(3,5),(4,5)],6)
 => [3,1]
 => [1]
 => 1
([(2,5),(3,4),(3,5),(4,5)],6)
 => [4]
 => []
 => ? = 0
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => [5]
 => []
 => ? = 0
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => [5]
 => []
 => ? = 0
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 0
([(0,5),(1,5),(2,4),(3,4)],6)
 => [2,2]
 => [2]
 => 1
([(0,5),(1,4),(2,3)],6)
 => [1,1,1]
 => [1,1]
 => 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => [3,1]
 => [1]
 => 1
([(1,2),(3,4),(3,5),(4,5)],6)
 => [3,1]
 => [1]
 => 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1]
 => [1]
 => 1
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => [4,1]
 => [1]
 => 1
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => [3,2]
 => [2]
 => 1
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => [3,3]
 => [3]
 => 1
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6,1]
 => [1]
 => 1
([(3,6),(4,5)],7)
 => [1,1]
 => [1]
 => 1
([(2,3),(4,6),(5,6)],7)
 => [2,1]
 => [1]
 => 1
([(1,2),(3,6),(4,6),(5,6)],7)
 => [3,1]
 => [1]
 => 1
([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
 => [4,1]
 => [1]
 => 1
([(1,6),(2,6),(3,5),(4,5)],7)
 => [2,2]
 => [2]
 => 1
([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
 => [3,2]
 => [2]
 => 1
([(1,6),(2,5),(3,4)],7)
 => [1,1,1]
 => [1,1]
 => 1
([(1,2),(3,6),(4,5),(5,6)],7)
 => [3,1]
 => [1]
 => 1
([(0,3),(1,2),(4,6),(5,6)],7)
 => [2,1,1]
 => [1,1]
 => 1
([(2,3),(4,5),(4,6),(5,6)],7)
 => [3,1]
 => [1]
 => 1
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
 => [4,1]
 => [1]
 => 1
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
 => [4,1]
 => [1]
 => 1
([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1]
 => 1
([(1,2),(3,5),(3,6),(4,5),(4,6)],7)
 => [4,1]
 => [1]
 => 1
([(0,6),(1,5),(2,4),(3,4),(5,6)],7)
 => [3,2]
 => [2]
 => 1
([(1,6),(2,6),(3,4),(3,5),(4,5)],7)
 => [3,2]
 => [2]
 => 1
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => [5,1]
 => [1]
 => 1
([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
 => [4,2]
 => [2]
 => 1
([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1]
 => 1
([(0,1),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1]
 => 1
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7)
 => [3,3]
 => [3]
 => 1
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7)
 => [4,2]
 => [2]
 => 1
([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7)
 => [5,2]
 => [2]
 => 1
([(0,1),(2,5),(3,4),(4,6),(5,6)],7)
 => [4,1]
 => [1]
 => 1
([(0,3),(1,2),(4,5),(4,6),(5,6)],7)
 => [3,1,1]
 => [1,1]
 => 1
([(0,1),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1]
 => 1
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5)],7)
 => [5,1]
 => [1]
 => 1
([(0,6),(1,5),(2,3),(2,4),(3,4),(5,6)],7)
 => [3,3]
 => [3]
 => 1
([(0,1),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1
([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7)
 => [3,3]
 => [3]
 => 1
([(0,1),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1
Description
The order dimension of the partition. Given a partition $\lambda$, let $I(\lambda)$ be the principal order ideal in the Young lattice generated by $\lambda$. The order dimension of a partition is defined as the order dimension of the poset $I(\lambda)$.
Matching statistic: St001609
Mapping
Mp00275: Graphs —to edge-partition of connected components⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001609: Integer partitions ⟶ ℤResult quality: 20% ●values known / values provided: 21%●distinct values known / distinct values provided: 20%
Values
([(0,1)],2)
 => [1]
 => []
 => ? = 0
([(1,2)],3)
 => [1]
 => []
 => ? = 0
([(0,2),(1,2)],3)
 => [2]
 => []
 => ? = 0
([(0,1),(0,2),(1,2)],3)
 => [3]
 => []
 => ? = 0
([(2,3)],4)
 => [1]
 => []
 => ? = 0
([(1,3),(2,3)],4)
 => [2]
 => []
 => ? = 0
([(0,3),(1,3),(2,3)],4)
 => [3]
 => []
 => ? = 0
([(0,3),(1,2)],4)
 => [1,1]
 => [1]
 => 1
([(0,3),(1,2),(2,3)],4)
 => [3]
 => []
 => ? = 0
([(1,2),(1,3),(2,3)],4)
 => [3]
 => []
 => ? = 0
([(0,3),(1,2),(1,3),(2,3)],4)
 => [4]
 => []
 => ? = 0
([(0,2),(0,3),(1,2),(1,3)],4)
 => [4]
 => []
 => ? = 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [5]
 => []
 => ? = 0
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [6]
 => []
 => ? = 1
([(3,4)],5)
 => [1]
 => []
 => ? = 0
([(2,4),(3,4)],5)
 => [2]
 => []
 => ? = 0
([(1,4),(2,4),(3,4)],5)
 => [3]
 => []
 => ? = 0
([(0,4),(1,4),(2,4),(3,4)],5)
 => [4]
 => []
 => ? = 0
([(1,4),(2,3)],5)
 => [1,1]
 => [1]
 => 1
([(1,4),(2,3),(3,4)],5)
 => [3]
 => []
 => ? = 0
([(0,1),(2,4),(3,4)],5)
 => [2,1]
 => [1]
 => 1
([(2,3),(2,4),(3,4)],5)
 => [3]
 => []
 => ? = 0
([(0,4),(1,4),(2,3),(3,4)],5)
 => [4]
 => []
 => ? = 0
([(1,4),(2,3),(2,4),(3,4)],5)
 => [4]
 => []
 => ? = 0
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 0
([(1,3),(1,4),(2,3),(2,4)],5)
 => [4]
 => []
 => ? = 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 0
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 0
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [6]
 => []
 => ? = 0
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [6]
 => []
 => ? = 2
([(0,4),(1,3),(2,3),(2,4)],5)
 => [4]
 => []
 => ? = 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => [3,1]
 => [1]
 => 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => [6]
 => []
 => ? = 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => [5]
 => []
 => ? = 2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [6]
 => []
 => ? = 2
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => [7]
 => []
 => ? = 2
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => [6]
 => []
 => ? = 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [6]
 => []
 => ? = 1
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [7]
 => []
 => ? = 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => [7]
 => []
 => ? = 3
([(4,5)],6)
 => [1]
 => []
 => ? = 0
([(3,5),(4,5)],6)
 => [2]
 => []
 => ? = 0
([(2,5),(3,5),(4,5)],6)
 => [3]
 => []
 => ? = 0
([(1,5),(2,5),(3,5),(4,5)],6)
 => [4]
 => []
 => ? = 0
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => [5]
 => []
 => ? = 0
([(2,5),(3,4)],6)
 => [1,1]
 => [1]
 => 1
([(2,5),(3,4),(4,5)],6)
 => [3]
 => []
 => ? = 0
([(1,2),(3,5),(4,5)],6)
 => [2,1]
 => [1]
 => 1
([(3,4),(3,5),(4,5)],6)
 => [3]
 => []
 => ? = 0
([(1,5),(2,5),(3,4),(4,5)],6)
 => [4]
 => []
 => ? = 0
([(0,1),(2,5),(3,5),(4,5)],6)
 => [3,1]
 => [1]
 => 1
([(2,5),(3,4),(3,5),(4,5)],6)
 => [4]
 => []
 => ? = 0
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => [5]
 => []
 => ? = 0
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => [5]
 => []
 => ? = 0
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 0
([(0,5),(1,5),(2,4),(3,4)],6)
 => [2,2]
 => [2]
 => 1
([(0,5),(1,4),(2,3)],6)
 => [1,1,1]
 => [1,1]
 => 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => [3,1]
 => [1]
 => 1
([(1,2),(3,4),(3,5),(4,5)],6)
 => [3,1]
 => [1]
 => 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1]
 => [1]
 => 1
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => [4,1]
 => [1]
 => 1
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => [3,2]
 => [2]
 => 1
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => [3,3]
 => [3]
 => 1
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6,1]
 => [1]
 => 1
([(3,6),(4,5)],7)
 => [1,1]
 => [1]
 => 1
([(2,3),(4,6),(5,6)],7)
 => [2,1]
 => [1]
 => 1
([(1,2),(3,6),(4,6),(5,6)],7)
 => [3,1]
 => [1]
 => 1
([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
 => [4,1]
 => [1]
 => 1
([(1,6),(2,6),(3,5),(4,5)],7)
 => [2,2]
 => [2]
 => 1
([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
 => [3,2]
 => [2]
 => 1
([(1,6),(2,5),(3,4)],7)
 => [1,1,1]
 => [1,1]
 => 1
([(1,2),(3,6),(4,5),(5,6)],7)
 => [3,1]
 => [1]
 => 1
([(0,3),(1,2),(4,6),(5,6)],7)
 => [2,1,1]
 => [1,1]
 => 1
([(2,3),(4,5),(4,6),(5,6)],7)
 => [3,1]
 => [1]
 => 1
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
 => [4,1]
 => [1]
 => 1
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
 => [4,1]
 => [1]
 => 1
([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1]
 => 1
([(1,2),(3,5),(3,6),(4,5),(4,6)],7)
 => [4,1]
 => [1]
 => 1
([(0,6),(1,5),(2,4),(3,4),(5,6)],7)
 => [3,2]
 => [2]
 => 1
([(1,6),(2,6),(3,4),(3,5),(4,5)],7)
 => [3,2]
 => [2]
 => 1
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => [5,1]
 => [1]
 => 1
([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
 => [4,2]
 => [2]
 => 1
([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1]
 => 1
([(0,1),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1]
 => 1
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7)
 => [3,3]
 => [3]
 => 1
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7)
 => [4,2]
 => [2]
 => 1
([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7)
 => [5,2]
 => [2]
 => 1
([(0,1),(2,5),(3,4),(4,6),(5,6)],7)
 => [4,1]
 => [1]
 => 1
([(0,3),(1,2),(4,5),(4,6),(5,6)],7)
 => [3,1,1]
 => [1,1]
 => 1
([(0,1),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1]
 => 1
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5)],7)
 => [5,1]
 => [1]
 => 1
([(0,6),(1,5),(2,3),(2,4),(3,4),(5,6)],7)
 => [3,3]
 => [3]
 => 1
([(0,1),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1
([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7)
 => [3,3]
 => [3]
 => 1
([(0,1),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1
Description
The number of coloured trees such that the multiplicities of colours are given by a partition. In particular, the value on the partition $(n)$ is the number of unlabelled trees on $n$ vertices, [[oeis:A000055]], whereas the value on the partition $(1^n)$ is the number of labelled trees [[oeis:A000272]].
Matching statistic: St001780
(load all 2 compositions to match this statistic)
Mapping
Mp00275: Graphs —to edge-partition of connected components⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001780: Integer partitions ⟶ ℤResult quality: 20% ●values known / values provided: 21%●distinct values known / distinct values provided: 20%
Values
([(0,1)],2)
 => [1]
 => []
 => ? = 0
([(1,2)],3)
 => [1]
 => []
 => ? = 0
([(0,2),(1,2)],3)
 => [2]
 => []
 => ? = 0
([(0,1),(0,2),(1,2)],3)
 => [3]
 => []
 => ? = 0
([(2,3)],4)
 => [1]
 => []
 => ? = 0
([(1,3),(2,3)],4)
 => [2]
 => []
 => ? = 0
([(0,3),(1,3),(2,3)],4)
 => [3]
 => []
 => ? = 0
([(0,3),(1,2)],4)
 => [1,1]
 => [1]
 => 1
([(0,3),(1,2),(2,3)],4)
 => [3]
 => []
 => ? = 0
([(1,2),(1,3),(2,3)],4)
 => [3]
 => []
 => ? = 0
([(0,3),(1,2),(1,3),(2,3)],4)
 => [4]
 => []
 => ? = 0
([(0,2),(0,3),(1,2),(1,3)],4)
 => [4]
 => []
 => ? = 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [5]
 => []
 => ? = 0
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [6]
 => []
 => ? = 1
([(3,4)],5)
 => [1]
 => []
 => ? = 0
([(2,4),(3,4)],5)
 => [2]
 => []
 => ? = 0
([(1,4),(2,4),(3,4)],5)
 => [3]
 => []
 => ? = 0
([(0,4),(1,4),(2,4),(3,4)],5)
 => [4]
 => []
 => ? = 0
([(1,4),(2,3)],5)
 => [1,1]
 => [1]
 => 1
([(1,4),(2,3),(3,4)],5)
 => [3]
 => []
 => ? = 0
([(0,1),(2,4),(3,4)],5)
 => [2,1]
 => [1]
 => 1
([(2,3),(2,4),(3,4)],5)
 => [3]
 => []
 => ? = 0
([(0,4),(1,4),(2,3),(3,4)],5)
 => [4]
 => []
 => ? = 0
([(1,4),(2,3),(2,4),(3,4)],5)
 => [4]
 => []
 => ? = 0
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 0
([(1,3),(1,4),(2,3),(2,4)],5)
 => [4]
 => []
 => ? = 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 0
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 0
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [6]
 => []
 => ? = 0
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [6]
 => []
 => ? = 2
([(0,4),(1,3),(2,3),(2,4)],5)
 => [4]
 => []
 => ? = 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => [3,1]
 => [1]
 => 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => [6]
 => []
 => ? = 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => [5]
 => []
 => ? = 2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [6]
 => []
 => ? = 2
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => [7]
 => []
 => ? = 2
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => [6]
 => []
 => ? = 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [6]
 => []
 => ? = 1
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [7]
 => []
 => ? = 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => [7]
 => []
 => ? = 3
([(4,5)],6)
 => [1]
 => []
 => ? = 0
([(3,5),(4,5)],6)
 => [2]
 => []
 => ? = 0
([(2,5),(3,5),(4,5)],6)
 => [3]
 => []
 => ? = 0
([(1,5),(2,5),(3,5),(4,5)],6)
 => [4]
 => []
 => ? = 0
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => [5]
 => []
 => ? = 0
([(2,5),(3,4)],6)
 => [1,1]
 => [1]
 => 1
([(2,5),(3,4),(4,5)],6)
 => [3]
 => []
 => ? = 0
([(1,2),(3,5),(4,5)],6)
 => [2,1]
 => [1]
 => 1
([(3,4),(3,5),(4,5)],6)
 => [3]
 => []
 => ? = 0
([(1,5),(2,5),(3,4),(4,5)],6)
 => [4]
 => []
 => ? = 0
([(0,1),(2,5),(3,5),(4,5)],6)
 => [3,1]
 => [1]
 => 1
([(2,5),(3,4),(3,5),(4,5)],6)
 => [4]
 => []
 => ? = 0
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => [5]
 => []
 => ? = 0
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => [5]
 => []
 => ? = 0
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 0
([(0,5),(1,5),(2,4),(3,4)],6)
 => [2,2]
 => [2]
 => 1
([(0,5),(1,4),(2,3)],6)
 => [1,1,1]
 => [1,1]
 => 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => [3,1]
 => [1]
 => 1
([(1,2),(3,4),(3,5),(4,5)],6)
 => [3,1]
 => [1]
 => 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1]
 => [1]
 => 1
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => [4,1]
 => [1]
 => 1
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => [3,2]
 => [2]
 => 1
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => [3,3]
 => [3]
 => 1
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6,1]
 => [1]
 => 1
([(3,6),(4,5)],7)
 => [1,1]
 => [1]
 => 1
([(2,3),(4,6),(5,6)],7)
 => [2,1]
 => [1]
 => 1
([(1,2),(3,6),(4,6),(5,6)],7)
 => [3,1]
 => [1]
 => 1
([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
 => [4,1]
 => [1]
 => 1
([(1,6),(2,6),(3,5),(4,5)],7)
 => [2,2]
 => [2]
 => 1
([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
 => [3,2]
 => [2]
 => 1
([(1,6),(2,5),(3,4)],7)
 => [1,1,1]
 => [1,1]
 => 1
([(1,2),(3,6),(4,5),(5,6)],7)
 => [3,1]
 => [1]
 => 1
([(0,3),(1,2),(4,6),(5,6)],7)
 => [2,1,1]
 => [1,1]
 => 1
([(2,3),(4,5),(4,6),(5,6)],7)
 => [3,1]
 => [1]
 => 1
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
 => [4,1]
 => [1]
 => 1
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
 => [4,1]
 => [1]
 => 1
([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1]
 => 1
([(1,2),(3,5),(3,6),(4,5),(4,6)],7)
 => [4,1]
 => [1]
 => 1
([(0,6),(1,5),(2,4),(3,4),(5,6)],7)
 => [3,2]
 => [2]
 => 1
([(1,6),(2,6),(3,4),(3,5),(4,5)],7)
 => [3,2]
 => [2]
 => 1
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => [5,1]
 => [1]
 => 1
([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
 => [4,2]
 => [2]
 => 1
([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1]
 => 1
([(0,1),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1]
 => 1
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7)
 => [3,3]
 => [3]
 => 1
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7)
 => [4,2]
 => [2]
 => 1
([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7)
 => [5,2]
 => [2]
 => 1
([(0,1),(2,5),(3,4),(4,6),(5,6)],7)
 => [4,1]
 => [1]
 => 1
([(0,3),(1,2),(4,5),(4,6),(5,6)],7)
 => [3,1,1]
 => [1,1]
 => 1
([(0,1),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1]
 => 1
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5)],7)
 => [5,1]
 => [1]
 => 1
([(0,6),(1,5),(2,3),(2,4),(3,4),(5,6)],7)
 => [3,3]
 => [3]
 => 1
([(0,1),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1
([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7)
 => [3,3]
 => [3]
 => 1
([(0,1),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1
Description
The order of promotion on the set of standard tableaux of given shape.
Matching statistic: St001899
(load all 2 compositions to match this statistic)
Mapping
Mp00275: Graphs —to edge-partition of connected components⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001899: Integer partitions ⟶ ℤResult quality: 20% ●values known / values provided: 21%●distinct values known / distinct values provided: 20%
Values
([(0,1)],2)
 => [1]
 => []
 => ? = 0
([(1,2)],3)
 => [1]
 => []
 => ? = 0
([(0,2),(1,2)],3)
 => [2]
 => []
 => ? = 0
([(0,1),(0,2),(1,2)],3)
 => [3]
 => []
 => ? = 0
([(2,3)],4)
 => [1]
 => []
 => ? = 0
([(1,3),(2,3)],4)
 => [2]
 => []
 => ? = 0
([(0,3),(1,3),(2,3)],4)
 => [3]
 => []
 => ? = 0
([(0,3),(1,2)],4)
 => [1,1]
 => [1]
 => 1
([(0,3),(1,2),(2,3)],4)
 => [3]
 => []
 => ? = 0
([(1,2),(1,3),(2,3)],4)
 => [3]
 => []
 => ? = 0
([(0,3),(1,2),(1,3),(2,3)],4)
 => [4]
 => []
 => ? = 0
([(0,2),(0,3),(1,2),(1,3)],4)
 => [4]
 => []
 => ? = 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [5]
 => []
 => ? = 0
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [6]
 => []
 => ? = 1
([(3,4)],5)
 => [1]
 => []
 => ? = 0
([(2,4),(3,4)],5)
 => [2]
 => []
 => ? = 0
([(1,4),(2,4),(3,4)],5)
 => [3]
 => []
 => ? = 0
([(0,4),(1,4),(2,4),(3,4)],5)
 => [4]
 => []
 => ? = 0
([(1,4),(2,3)],5)
 => [1,1]
 => [1]
 => 1
([(1,4),(2,3),(3,4)],5)
 => [3]
 => []
 => ? = 0
([(0,1),(2,4),(3,4)],5)
 => [2,1]
 => [1]
 => 1
([(2,3),(2,4),(3,4)],5)
 => [3]
 => []
 => ? = 0
([(0,4),(1,4),(2,3),(3,4)],5)
 => [4]
 => []
 => ? = 0
([(1,4),(2,3),(2,4),(3,4)],5)
 => [4]
 => []
 => ? = 0
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 0
([(1,3),(1,4),(2,3),(2,4)],5)
 => [4]
 => []
 => ? = 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 0
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 0
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [6]
 => []
 => ? = 0
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [6]
 => []
 => ? = 2
([(0,4),(1,3),(2,3),(2,4)],5)
 => [4]
 => []
 => ? = 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => [3,1]
 => [1]
 => 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => [6]
 => []
 => ? = 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => [5]
 => []
 => ? = 2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [6]
 => []
 => ? = 2
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => [7]
 => []
 => ? = 2
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => [6]
 => []
 => ? = 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [6]
 => []
 => ? = 1
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [7]
 => []
 => ? = 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => [7]
 => []
 => ? = 3
([(4,5)],6)
 => [1]
 => []
 => ? = 0
([(3,5),(4,5)],6)
 => [2]
 => []
 => ? = 0
([(2,5),(3,5),(4,5)],6)
 => [3]
 => []
 => ? = 0
([(1,5),(2,5),(3,5),(4,5)],6)
 => [4]
 => []
 => ? = 0
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => [5]
 => []
 => ? = 0
([(2,5),(3,4)],6)
 => [1,1]
 => [1]
 => 1
([(2,5),(3,4),(4,5)],6)
 => [3]
 => []
 => ? = 0
([(1,2),(3,5),(4,5)],6)
 => [2,1]
 => [1]
 => 1
([(3,4),(3,5),(4,5)],6)
 => [3]
 => []
 => ? = 0
([(1,5),(2,5),(3,4),(4,5)],6)
 => [4]
 => []
 => ? = 0
([(0,1),(2,5),(3,5),(4,5)],6)
 => [3,1]
 => [1]
 => 1
([(2,5),(3,4),(3,5),(4,5)],6)
 => [4]
 => []
 => ? = 0
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => [5]
 => []
 => ? = 0
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => [5]
 => []
 => ? = 0
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 0
([(0,5),(1,5),(2,4),(3,4)],6)
 => [2,2]
 => [2]
 => 1
([(0,5),(1,4),(2,3)],6)
 => [1,1,1]
 => [1,1]
 => 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => [3,1]
 => [1]
 => 1
([(1,2),(3,4),(3,5),(4,5)],6)
 => [3,1]
 => [1]
 => 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1]
 => [1]
 => 1
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => [4,1]
 => [1]
 => 1
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => [3,2]
 => [2]
 => 1
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => [3,3]
 => [3]
 => 1
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6,1]
 => [1]
 => 1
([(3,6),(4,5)],7)
 => [1,1]
 => [1]
 => 1
([(2,3),(4,6),(5,6)],7)
 => [2,1]
 => [1]
 => 1
([(1,2),(3,6),(4,6),(5,6)],7)
 => [3,1]
 => [1]
 => 1
([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
 => [4,1]
 => [1]
 => 1
([(1,6),(2,6),(3,5),(4,5)],7)
 => [2,2]
 => [2]
 => 1
([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
 => [3,2]
 => [2]
 => 1
([(1,6),(2,5),(3,4)],7)
 => [1,1,1]
 => [1,1]
 => 1
([(1,2),(3,6),(4,5),(5,6)],7)
 => [3,1]
 => [1]
 => 1
([(0,3),(1,2),(4,6),(5,6)],7)
 => [2,1,1]
 => [1,1]
 => 1
([(2,3),(4,5),(4,6),(5,6)],7)
 => [3,1]
 => [1]
 => 1
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
 => [4,1]
 => [1]
 => 1
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
 => [4,1]
 => [1]
 => 1
([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1]
 => 1
([(1,2),(3,5),(3,6),(4,5),(4,6)],7)
 => [4,1]
 => [1]
 => 1
([(0,6),(1,5),(2,4),(3,4),(5,6)],7)
 => [3,2]
 => [2]
 => 1
([(1,6),(2,6),(3,4),(3,5),(4,5)],7)
 => [3,2]
 => [2]
 => 1
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => [5,1]
 => [1]
 => 1
([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
 => [4,2]
 => [2]
 => 1
([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1]
 => 1
([(0,1),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1]
 => 1
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7)
 => [3,3]
 => [3]
 => 1
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7)
 => [4,2]
 => [2]
 => 1
([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7)
 => [5,2]
 => [2]
 => 1
([(0,1),(2,5),(3,4),(4,6),(5,6)],7)
 => [4,1]
 => [1]
 => 1
([(0,3),(1,2),(4,5),(4,6),(5,6)],7)
 => [3,1,1]
 => [1,1]
 => 1
([(0,1),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1]
 => 1
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5)],7)
 => [5,1]
 => [1]
 => 1
([(0,6),(1,5),(2,3),(2,4),(3,4),(5,6)],7)
 => [3,3]
 => [3]
 => 1
([(0,1),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1
([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7)
 => [3,3]
 => [3]
 => 1
([(0,1),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1
Description
The total number of irreducible representations contained in the higher Lie character for an integer partition.
Matching statistic: St001900
(load all 2 compositions to match this statistic)
Mapping
Mp00275: Graphs —to edge-partition of connected components⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001900: Integer partitions ⟶ ℤResult quality: 20% ●values known / values provided: 21%●distinct values known / distinct values provided: 20%
Values
([(0,1)],2)
 => [1]
 => []
 => ? = 0
([(1,2)],3)
 => [1]
 => []
 => ? = 0
([(0,2),(1,2)],3)
 => [2]
 => []
 => ? = 0
([(0,1),(0,2),(1,2)],3)
 => [3]
 => []
 => ? = 0
([(2,3)],4)
 => [1]
 => []
 => ? = 0
([(1,3),(2,3)],4)
 => [2]
 => []
 => ? = 0
([(0,3),(1,3),(2,3)],4)
 => [3]
 => []
 => ? = 0
([(0,3),(1,2)],4)
 => [1,1]
 => [1]
 => 1
([(0,3),(1,2),(2,3)],4)
 => [3]
 => []
 => ? = 0
([(1,2),(1,3),(2,3)],4)
 => [3]
 => []
 => ? = 0
([(0,3),(1,2),(1,3),(2,3)],4)
 => [4]
 => []
 => ? = 0
([(0,2),(0,3),(1,2),(1,3)],4)
 => [4]
 => []
 => ? = 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [5]
 => []
 => ? = 0
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [6]
 => []
 => ? = 1
([(3,4)],5)
 => [1]
 => []
 => ? = 0
([(2,4),(3,4)],5)
 => [2]
 => []
 => ? = 0
([(1,4),(2,4),(3,4)],5)
 => [3]
 => []
 => ? = 0
([(0,4),(1,4),(2,4),(3,4)],5)
 => [4]
 => []
 => ? = 0
([(1,4),(2,3)],5)
 => [1,1]
 => [1]
 => 1
([(1,4),(2,3),(3,4)],5)
 => [3]
 => []
 => ? = 0
([(0,1),(2,4),(3,4)],5)
 => [2,1]
 => [1]
 => 1
([(2,3),(2,4),(3,4)],5)
 => [3]
 => []
 => ? = 0
([(0,4),(1,4),(2,3),(3,4)],5)
 => [4]
 => []
 => ? = 0
([(1,4),(2,3),(2,4),(3,4)],5)
 => [4]
 => []
 => ? = 0
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 0
([(1,3),(1,4),(2,3),(2,4)],5)
 => [4]
 => []
 => ? = 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 0
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 0
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [6]
 => []
 => ? = 0
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [6]
 => []
 => ? = 2
([(0,4),(1,3),(2,3),(2,4)],5)
 => [4]
 => []
 => ? = 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => [3,1]
 => [1]
 => 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => [6]
 => []
 => ? = 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => [5]
 => []
 => ? = 2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [6]
 => []
 => ? = 2
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => [7]
 => []
 => ? = 2
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => [6]
 => []
 => ? = 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [6]
 => []
 => ? = 1
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [7]
 => []
 => ? = 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => [7]
 => []
 => ? = 3
([(4,5)],6)
 => [1]
 => []
 => ? = 0
([(3,5),(4,5)],6)
 => [2]
 => []
 => ? = 0
([(2,5),(3,5),(4,5)],6)
 => [3]
 => []
 => ? = 0
([(1,5),(2,5),(3,5),(4,5)],6)
 => [4]
 => []
 => ? = 0
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => [5]
 => []
 => ? = 0
([(2,5),(3,4)],6)
 => [1,1]
 => [1]
 => 1
([(2,5),(3,4),(4,5)],6)
 => [3]
 => []
 => ? = 0
([(1,2),(3,5),(4,5)],6)
 => [2,1]
 => [1]
 => 1
([(3,4),(3,5),(4,5)],6)
 => [3]
 => []
 => ? = 0
([(1,5),(2,5),(3,4),(4,5)],6)
 => [4]
 => []
 => ? = 0
([(0,1),(2,5),(3,5),(4,5)],6)
 => [3,1]
 => [1]
 => 1
([(2,5),(3,4),(3,5),(4,5)],6)
 => [4]
 => []
 => ? = 0
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => [5]
 => []
 => ? = 0
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => [5]
 => []
 => ? = 0
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 0
([(0,5),(1,5),(2,4),(3,4)],6)
 => [2,2]
 => [2]
 => 1
([(0,5),(1,4),(2,3)],6)
 => [1,1,1]
 => [1,1]
 => 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => [3,1]
 => [1]
 => 1
([(1,2),(3,4),(3,5),(4,5)],6)
 => [3,1]
 => [1]
 => 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1]
 => [1]
 => 1
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => [4,1]
 => [1]
 => 1
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => [3,2]
 => [2]
 => 1
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => [3,3]
 => [3]
 => 1
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6,1]
 => [1]
 => 1
([(3,6),(4,5)],7)
 => [1,1]
 => [1]
 => 1
([(2,3),(4,6),(5,6)],7)
 => [2,1]
 => [1]
 => 1
([(1,2),(3,6),(4,6),(5,6)],7)
 => [3,1]
 => [1]
 => 1
([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
 => [4,1]
 => [1]
 => 1
([(1,6),(2,6),(3,5),(4,5)],7)
 => [2,2]
 => [2]
 => 1
([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
 => [3,2]
 => [2]
 => 1
([(1,6),(2,5),(3,4)],7)
 => [1,1,1]
 => [1,1]
 => 1
([(1,2),(3,6),(4,5),(5,6)],7)
 => [3,1]
 => [1]
 => 1
([(0,3),(1,2),(4,6),(5,6)],7)
 => [2,1,1]
 => [1,1]
 => 1
([(2,3),(4,5),(4,6),(5,6)],7)
 => [3,1]
 => [1]
 => 1
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
 => [4,1]
 => [1]
 => 1
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
 => [4,1]
 => [1]
 => 1
([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1]
 => 1
([(1,2),(3,5),(3,6),(4,5),(4,6)],7)
 => [4,1]
 => [1]
 => 1
([(0,6),(1,5),(2,4),(3,4),(5,6)],7)
 => [3,2]
 => [2]
 => 1
([(1,6),(2,6),(3,4),(3,5),(4,5)],7)
 => [3,2]
 => [2]
 => 1
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => [5,1]
 => [1]
 => 1
([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
 => [4,2]
 => [2]
 => 1
([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1]
 => 1
([(0,1),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1]
 => 1
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7)
 => [3,3]
 => [3]
 => 1
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7)
 => [4,2]
 => [2]
 => 1
([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7)
 => [5,2]
 => [2]
 => 1
([(0,1),(2,5),(3,4),(4,6),(5,6)],7)
 => [4,1]
 => [1]
 => 1
([(0,3),(1,2),(4,5),(4,6),(5,6)],7)
 => [3,1,1]
 => [1,1]
 => 1
([(0,1),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1]
 => 1
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5)],7)
 => [5,1]
 => [1]
 => 1
([(0,6),(1,5),(2,3),(2,4),(3,4),(5,6)],7)
 => [3,3]
 => [3]
 => 1
([(0,1),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1
([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7)
 => [3,3]
 => [3]
 => 1
([(0,1),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1
Description
The number of distinct irreducible representations contained in the higher Lie character for an integer partition.
Matching statistic: St001901
(load all 2 compositions to match this statistic)
Mapping
Mp00275: Graphs —to edge-partition of connected components⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001901: Integer partitions ⟶ ℤResult quality: 20% ●values known / values provided: 21%●distinct values known / distinct values provided: 20%
Values
([(0,1)],2)
 => [1]
 => []
 => ? = 0
([(1,2)],3)
 => [1]
 => []
 => ? = 0
([(0,2),(1,2)],3)
 => [2]
 => []
 => ? = 0
([(0,1),(0,2),(1,2)],3)
 => [3]
 => []
 => ? = 0
([(2,3)],4)
 => [1]
 => []
 => ? = 0
([(1,3),(2,3)],4)
 => [2]
 => []
 => ? = 0
([(0,3),(1,3),(2,3)],4)
 => [3]
 => []
 => ? = 0
([(0,3),(1,2)],4)
 => [1,1]
 => [1]
 => 1
([(0,3),(1,2),(2,3)],4)
 => [3]
 => []
 => ? = 0
([(1,2),(1,3),(2,3)],4)
 => [3]
 => []
 => ? = 0
([(0,3),(1,2),(1,3),(2,3)],4)
 => [4]
 => []
 => ? = 0
([(0,2),(0,3),(1,2),(1,3)],4)
 => [4]
 => []
 => ? = 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [5]
 => []
 => ? = 0
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [6]
 => []
 => ? = 1
([(3,4)],5)
 => [1]
 => []
 => ? = 0
([(2,4),(3,4)],5)
 => [2]
 => []
 => ? = 0
([(1,4),(2,4),(3,4)],5)
 => [3]
 => []
 => ? = 0
([(0,4),(1,4),(2,4),(3,4)],5)
 => [4]
 => []
 => ? = 0
([(1,4),(2,3)],5)
 => [1,1]
 => [1]
 => 1
([(1,4),(2,3),(3,4)],5)
 => [3]
 => []
 => ? = 0
([(0,1),(2,4),(3,4)],5)
 => [2,1]
 => [1]
 => 1
([(2,3),(2,4),(3,4)],5)
 => [3]
 => []
 => ? = 0
([(0,4),(1,4),(2,3),(3,4)],5)
 => [4]
 => []
 => ? = 0
([(1,4),(2,3),(2,4),(3,4)],5)
 => [4]
 => []
 => ? = 0
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 0
([(1,3),(1,4),(2,3),(2,4)],5)
 => [4]
 => []
 => ? = 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 0
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 0
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [6]
 => []
 => ? = 0
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [6]
 => []
 => ? = 2
([(0,4),(1,3),(2,3),(2,4)],5)
 => [4]
 => []
 => ? = 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => [3,1]
 => [1]
 => 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => [6]
 => []
 => ? = 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => [5]
 => []
 => ? = 2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [6]
 => []
 => ? = 2
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => [7]
 => []
 => ? = 2
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => [6]
 => []
 => ? = 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [6]
 => []
 => ? = 1
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [7]
 => []
 => ? = 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => [7]
 => []
 => ? = 3
([(4,5)],6)
 => [1]
 => []
 => ? = 0
([(3,5),(4,5)],6)
 => [2]
 => []
 => ? = 0
([(2,5),(3,5),(4,5)],6)
 => [3]
 => []
 => ? = 0
([(1,5),(2,5),(3,5),(4,5)],6)
 => [4]
 => []
 => ? = 0
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => [5]
 => []
 => ? = 0
([(2,5),(3,4)],6)
 => [1,1]
 => [1]
 => 1
([(2,5),(3,4),(4,5)],6)
 => [3]
 => []
 => ? = 0
([(1,2),(3,5),(4,5)],6)
 => [2,1]
 => [1]
 => 1
([(3,4),(3,5),(4,5)],6)
 => [3]
 => []
 => ? = 0
([(1,5),(2,5),(3,4),(4,5)],6)
 => [4]
 => []
 => ? = 0
([(0,1),(2,5),(3,5),(4,5)],6)
 => [3,1]
 => [1]
 => 1
([(2,5),(3,4),(3,5),(4,5)],6)
 => [4]
 => []
 => ? = 0
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => [5]
 => []
 => ? = 0
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => [5]
 => []
 => ? = 0
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 0
([(0,5),(1,5),(2,4),(3,4)],6)
 => [2,2]
 => [2]
 => 1
([(0,5),(1,4),(2,3)],6)
 => [1,1,1]
 => [1,1]
 => 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => [3,1]
 => [1]
 => 1
([(1,2),(3,4),(3,5),(4,5)],6)
 => [3,1]
 => [1]
 => 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1]
 => [1]
 => 1
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => [4,1]
 => [1]
 => 1
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => [3,2]
 => [2]
 => 1
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => [3,3]
 => [3]
 => 1
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6,1]
 => [1]
 => 1
([(3,6),(4,5)],7)
 => [1,1]
 => [1]
 => 1
([(2,3),(4,6),(5,6)],7)
 => [2,1]
 => [1]
 => 1
([(1,2),(3,6),(4,6),(5,6)],7)
 => [3,1]
 => [1]
 => 1
([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
 => [4,1]
 => [1]
 => 1
([(1,6),(2,6),(3,5),(4,5)],7)
 => [2,2]
 => [2]
 => 1
([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
 => [3,2]
 => [2]
 => 1
([(1,6),(2,5),(3,4)],7)
 => [1,1,1]
 => [1,1]
 => 1
([(1,2),(3,6),(4,5),(5,6)],7)
 => [3,1]
 => [1]
 => 1
([(0,3),(1,2),(4,6),(5,6)],7)
 => [2,1,1]
 => [1,1]
 => 1
([(2,3),(4,5),(4,6),(5,6)],7)
 => [3,1]
 => [1]
 => 1
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
 => [4,1]
 => [1]
 => 1
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
 => [4,1]
 => [1]
 => 1
([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1]
 => 1
([(1,2),(3,5),(3,6),(4,5),(4,6)],7)
 => [4,1]
 => [1]
 => 1
([(0,6),(1,5),(2,4),(3,4),(5,6)],7)
 => [3,2]
 => [2]
 => 1
([(1,6),(2,6),(3,4),(3,5),(4,5)],7)
 => [3,2]
 => [2]
 => 1
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => [5,1]
 => [1]
 => 1
([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
 => [4,2]
 => [2]
 => 1
([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1]
 => 1
([(0,1),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1]
 => 1
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7)
 => [3,3]
 => [3]
 => 1
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7)
 => [4,2]
 => [2]
 => 1
([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7)
 => [5,2]
 => [2]
 => 1
([(0,1),(2,5),(3,4),(4,6),(5,6)],7)
 => [4,1]
 => [1]
 => 1
([(0,3),(1,2),(4,5),(4,6),(5,6)],7)
 => [3,1,1]
 => [1,1]
 => 1
([(0,1),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1]
 => 1
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5)],7)
 => [5,1]
 => [1]
 => 1
([(0,6),(1,5),(2,3),(2,4),(3,4),(5,6)],7)
 => [3,3]
 => [3]
 => 1
([(0,1),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1
([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7)
 => [3,3]
 => [3]
 => 1
([(0,1),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1
Description
The largest multiplicity of an irreducible representation contained in the higher Lie character for an integer partition.
Matching statistic: St001908
(load all 2 compositions to match this statistic)
Mapping
Mp00275: Graphs —to edge-partition of connected components⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001908: Integer partitions ⟶ ℤResult quality: 20% ●values known / values provided: 21%●distinct values known / distinct values provided: 20%
Values
([(0,1)],2)
 => [1]
 => []
 => ? = 0
([(1,2)],3)
 => [1]
 => []
 => ? = 0
([(0,2),(1,2)],3)
 => [2]
 => []
 => ? = 0
([(0,1),(0,2),(1,2)],3)
 => [3]
 => []
 => ? = 0
([(2,3)],4)
 => [1]
 => []
 => ? = 0
([(1,3),(2,3)],4)
 => [2]
 => []
 => ? = 0
([(0,3),(1,3),(2,3)],4)
 => [3]
 => []
 => ? = 0
([(0,3),(1,2)],4)
 => [1,1]
 => [1]
 => 1
([(0,3),(1,2),(2,3)],4)
 => [3]
 => []
 => ? = 0
([(1,2),(1,3),(2,3)],4)
 => [3]
 => []
 => ? = 0
([(0,3),(1,2),(1,3),(2,3)],4)
 => [4]
 => []
 => ? = 0
([(0,2),(0,3),(1,2),(1,3)],4)
 => [4]
 => []
 => ? = 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [5]
 => []
 => ? = 0
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [6]
 => []
 => ? = 1
([(3,4)],5)
 => [1]
 => []
 => ? = 0
([(2,4),(3,4)],5)
 => [2]
 => []
 => ? = 0
([(1,4),(2,4),(3,4)],5)
 => [3]
 => []
 => ? = 0
([(0,4),(1,4),(2,4),(3,4)],5)
 => [4]
 => []
 => ? = 0
([(1,4),(2,3)],5)
 => [1,1]
 => [1]
 => 1
([(1,4),(2,3),(3,4)],5)
 => [3]
 => []
 => ? = 0
([(0,1),(2,4),(3,4)],5)
 => [2,1]
 => [1]
 => 1
([(2,3),(2,4),(3,4)],5)
 => [3]
 => []
 => ? = 0
([(0,4),(1,4),(2,3),(3,4)],5)
 => [4]
 => []
 => ? = 0
([(1,4),(2,3),(2,4),(3,4)],5)
 => [4]
 => []
 => ? = 0
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 0
([(1,3),(1,4),(2,3),(2,4)],5)
 => [4]
 => []
 => ? = 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 0
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 0
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [6]
 => []
 => ? = 0
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [6]
 => []
 => ? = 2
([(0,4),(1,3),(2,3),(2,4)],5)
 => [4]
 => []
 => ? = 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => [3,1]
 => [1]
 => 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => [6]
 => []
 => ? = 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => [5]
 => []
 => ? = 2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [6]
 => []
 => ? = 2
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => [7]
 => []
 => ? = 2
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => [6]
 => []
 => ? = 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [6]
 => []
 => ? = 1
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [7]
 => []
 => ? = 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => [7]
 => []
 => ? = 3
([(4,5)],6)
 => [1]
 => []
 => ? = 0
([(3,5),(4,5)],6)
 => [2]
 => []
 => ? = 0
([(2,5),(3,5),(4,5)],6)
 => [3]
 => []
 => ? = 0
([(1,5),(2,5),(3,5),(4,5)],6)
 => [4]
 => []
 => ? = 0
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => [5]
 => []
 => ? = 0
([(2,5),(3,4)],6)
 => [1,1]
 => [1]
 => 1
([(2,5),(3,4),(4,5)],6)
 => [3]
 => []
 => ? = 0
([(1,2),(3,5),(4,5)],6)
 => [2,1]
 => [1]
 => 1
([(3,4),(3,5),(4,5)],6)
 => [3]
 => []
 => ? = 0
([(1,5),(2,5),(3,4),(4,5)],6)
 => [4]
 => []
 => ? = 0
([(0,1),(2,5),(3,5),(4,5)],6)
 => [3,1]
 => [1]
 => 1
([(2,5),(3,4),(3,5),(4,5)],6)
 => [4]
 => []
 => ? = 0
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => [5]
 => []
 => ? = 0
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => [5]
 => []
 => ? = 0
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 0
([(0,5),(1,5),(2,4),(3,4)],6)
 => [2,2]
 => [2]
 => 1
([(0,5),(1,4),(2,3)],6)
 => [1,1,1]
 => [1,1]
 => 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => [3,1]
 => [1]
 => 1
([(1,2),(3,4),(3,5),(4,5)],6)
 => [3,1]
 => [1]
 => 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1]
 => [1]
 => 1
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => [4,1]
 => [1]
 => 1
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => [3,2]
 => [2]
 => 1
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => [3,3]
 => [3]
 => 1
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6,1]
 => [1]
 => 1
([(3,6),(4,5)],7)
 => [1,1]
 => [1]
 => 1
([(2,3),(4,6),(5,6)],7)
 => [2,1]
 => [1]
 => 1
([(1,2),(3,6),(4,6),(5,6)],7)
 => [3,1]
 => [1]
 => 1
([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
 => [4,1]
 => [1]
 => 1
([(1,6),(2,6),(3,5),(4,5)],7)
 => [2,2]
 => [2]
 => 1
([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
 => [3,2]
 => [2]
 => 1
([(1,6),(2,5),(3,4)],7)
 => [1,1,1]
 => [1,1]
 => 1
([(1,2),(3,6),(4,5),(5,6)],7)
 => [3,1]
 => [1]
 => 1
([(0,3),(1,2),(4,6),(5,6)],7)
 => [2,1,1]
 => [1,1]
 => 1
([(2,3),(4,5),(4,6),(5,6)],7)
 => [3,1]
 => [1]
 => 1
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
 => [4,1]
 => [1]
 => 1
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
 => [4,1]
 => [1]
 => 1
([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1]
 => 1
([(1,2),(3,5),(3,6),(4,5),(4,6)],7)
 => [4,1]
 => [1]
 => 1
([(0,6),(1,5),(2,4),(3,4),(5,6)],7)
 => [3,2]
 => [2]
 => 1
([(1,6),(2,6),(3,4),(3,5),(4,5)],7)
 => [3,2]
 => [2]
 => 1
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => [5,1]
 => [1]
 => 1
([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
 => [4,2]
 => [2]
 => 1
([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1]
 => 1
([(0,1),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1]
 => 1
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7)
 => [3,3]
 => [3]
 => 1
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7)
 => [4,2]
 => [2]
 => 1
([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7)
 => [5,2]
 => [2]
 => 1
([(0,1),(2,5),(3,4),(4,6),(5,6)],7)
 => [4,1]
 => [1]
 => 1
([(0,3),(1,2),(4,5),(4,6),(5,6)],7)
 => [3,1,1]
 => [1,1]
 => 1
([(0,1),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1]
 => 1
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5)],7)
 => [5,1]
 => [1]
 => 1
([(0,6),(1,5),(2,3),(2,4),(3,4),(5,6)],7)
 => [3,3]
 => [3]
 => 1
([(0,1),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1
([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7)
 => [3,3]
 => [3]
 => 1
([(0,1),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1
Description
The number of semistandard tableaux of distinct weight whose maximal entry is the length of the partition. For example, there are eight tableaux of shape $[3,2,1]$ with maximal entry $3$, but two of them have the same weight.
The following 18 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St001913The number of preimages of an integer partition in Bulgarian solitaire. St001924The number of cells in an integer partition whose arm and leg length coincide. St001936The number of transitive factorisations of a permutation of given cycle type into star transpositions. St000175Degree of the polynomial counting the number of semistandard Young tableaux when stretching the shape. St000205Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and partition weight. St000206Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and integer composition weight. St000225Difference between largest and smallest parts in a partition. St000749The smallest integer d such that the restriction of the representation corresponding to a partition of n to the symmetric group on n-d letters has a constituent of odd degree. St001175The size of a partition minus the hook length of the base cell. St001178Twelve times the variance of the major index among all standard Young tableaux of a partition. St001586The number of odd parts smaller than the largest even part in an integer partition. St001568The smallest positive integer that does not appear twice in the partition. St001599The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on rooted trees. St001934The number of monotone factorisations of genus zero of a permutation of given cycle type. St000929The constant term of the character polynomial of an integer partition. St000944The 3-degree of an integer partition. St001198The number of simple modules in the algebra $eAe$ with projective dimension at most 1 in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001206The maximal dimension of an indecomposable projective $eAe$-module (that is the height of the corresponding Dyck path) of the corresponding Nakayama algebra with minimal faithful projective-injective module $eA$.