Processing math: 100%

Your data matches 70 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000298
(load all 4 compositions to match this statistic)
Mapping
St000298: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => 1
([],2)
 => 2
([(0,1)],2)
 => 1
([],3)
 => 2
([(1,2)],3)
 => 2
([(0,1),(0,2)],3)
 => 2
([(0,2),(2,1)],3)
 => 1
([(0,2),(1,2)],3)
 => 2
([],4)
 => 2
([(2,3)],4)
 => 2
([(1,2),(1,3)],4)
 => 2
([(0,1),(0,2),(0,3)],4)
 => 2
([(0,2),(0,3),(3,1)],4)
 => 2
([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(1,2),(2,3)],4)
 => 2
([(0,3),(3,1),(3,2)],4)
 => 2
([(1,3),(2,3)],4)
 => 2
([(0,3),(1,3),(3,2)],4)
 => 2
([(0,3),(1,3),(2,3)],4)
 => 2
([(0,3),(1,2)],4)
 => 2
([(0,3),(1,2),(1,3)],4)
 => 2
([(0,2),(0,3),(1,2),(1,3)],4)
 => 2
([(0,3),(2,1),(3,2)],4)
 => 1
([(0,3),(1,2),(2,3)],4)
 => 2
([],5)
 => 2
([(3,4)],5)
 => 2
([(2,3),(2,4)],5)
 => 2
([(1,2),(1,3),(1,4)],5)
 => 2
([(0,1),(0,2),(0,3),(0,4)],5)
 => 2
([(0,2),(0,3),(0,4),(4,1)],5)
 => 2
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => 2
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(1,3),(1,4),(4,2)],5)
 => 2
([(0,3),(0,4),(4,1),(4,2)],5)
 => 2
([(1,2),(1,3),(2,4),(3,4)],5)
 => 2
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 2
([(0,3),(0,4),(3,2),(4,1)],5)
 => 2
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => 2
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => 2
([(2,3),(3,4)],5)
 => 2
([(1,4),(4,2),(4,3)],5)
 => 2
([(0,4),(4,1),(4,2),(4,3)],5)
 => 2
([(2,4),(3,4)],5)
 => 2
([(1,4),(2,4),(4,3)],5)
 => 2
([(0,4),(1,4),(4,2),(4,3)],5)
 => 2
([(1,4),(2,4),(3,4)],5)
 => 2
([(0,4),(1,4),(2,4),(4,3)],5)
 => 2
([(0,4),(1,4),(2,4),(3,4)],5)
 => 2
([(0,4),(1,4),(2,3)],5)
 => 2
([(0,4),(1,3),(2,3),(2,4)],5)
 => 2
Description
The order dimension or Dushnik-Miller dimension of a poset. This is the minimal number of linear orderings whose intersection is the given poset.
Matching statistic: St001890
(load all 3 compositions to match this statistic)
Mapping
Mp00198: Posets —incomparability graph⟶ Graphs
Mp00157: Graphs —connected complement⟶ Graphs
Mp00243: Graphs —weak duplicate order⟶ Posets
St001890: Posets ⟶ ℤResult quality: 33% ●values known / values provided: 37%●distinct values known / distinct values provided: 33%
Values
([],1)
 => ([],1)
 => ([],1)
 => ([],1)
 => ? = 1 - 1
([],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 1 = 2 - 1
([(0,1)],2)
 => ([],2)
 => ([],2)
 => ([],1)
 => ? = 1 - 1
([],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => 1 = 2 - 1
([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([],2)
 => 1 = 2 - 1
([(0,1),(0,2)],3)
 => ([(1,2)],3)
 => ([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 1 = 2 - 1
([(0,2),(2,1)],3)
 => ([],3)
 => ([],3)
 => ([],1)
 => ? = 1 - 1
([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => ([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 1 = 2 - 1
([],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => 1 = 2 - 1
([(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],3)
 => 1 = 2 - 1
([(1,2),(1,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => 1 = 2 - 1
([(0,1),(0,2),(0,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => 1 = 2 - 1
([(0,2),(0,3),(3,1)],4)
 => ([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,2),(1,2)],3)
 => 1 = 2 - 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ([(2,3)],4)
 => ([(0,2),(1,2)],3)
 => 1 = 2 - 1
([(1,2),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([],2)
 => 1 = 2 - 1
([(0,3),(3,1),(3,2)],4)
 => ([(2,3)],4)
 => ([(2,3)],4)
 => ([(0,2),(1,2)],3)
 => 1 = 2 - 1
([(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => 1 = 2 - 1
([(0,3),(1,3),(3,2)],4)
 => ([(2,3)],4)
 => ([(2,3)],4)
 => ([(0,2),(1,2)],3)
 => 1 = 2 - 1
([(0,3),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => 1 = 2 - 1
([(0,3),(1,2)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([],2)
 => 1 = 2 - 1
([(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2)],4)
 => 1 = 2 - 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => ([],4)
 => 1 = 2 - 1
([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ([],4)
 => ([],1)
 => ? = 1 - 1
([(0,3),(1,2),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,2),(1,2)],3)
 => 1 = 2 - 1
([],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => 1 = 2 - 1
([(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],4)
 => 1 = 2 - 1
([(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(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)
 => 1 = 2 - 1
([(1,2),(1,3),(1,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,1),(0,2),(0,3),(0,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,2),(0,3),(0,4),(4,1)],5)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(1,3),(2,3)],4)
 => 1 = 2 - 1
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => 1 = 2 - 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,3),(1,3),(2,3)],4)
 => 1 = 2 - 1
([(1,3),(1,4),(4,2)],5)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => 1 = 2 - 1
([(0,3),(0,4),(4,1),(4,2)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => 1 = 2 - 1
([(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => 1 = 2 - 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(3,4)],5)
 => ([(3,4)],5)
 => ([(0,2),(1,2)],3)
 => 1 = 2 - 1
([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,2),(1,2)],3)
 => 1 = 2 - 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,4),(2,3)],5)
 => ([(1,4),(2,3)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(2,3),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],3)
 => 1 = 2 - 1
([(1,4),(4,2),(4,3)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => 1 = 2 - 1
([(0,4),(4,1),(4,2),(4,3)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,3),(1,3),(2,3)],4)
 => 1 = 2 - 1
([(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(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)
 => 1 = 2 - 1
([(1,4),(2,4),(4,3)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => 1 = 2 - 1
([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(1,4),(2,3)],5)
 => ([(1,4),(2,3)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,4),(1,4),(2,4),(4,3)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,3),(1,3),(2,3)],4)
 => 1 = 2 - 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,4),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,3),(2,3)],4)
 => 1 = 2 - 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(2,3),(2,4)],5)
 => 1 = 2 - 1
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,3),(1,2)],4)
 => 1 = 2 - 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => 1 = 2 - 1
([(0,4),(1,4),(2,3),(4,2)],5)
 => ([(3,4)],5)
 => ([(3,4)],5)
 => ([(0,2),(1,2)],3)
 => 1 = 2 - 1
([(0,4),(1,3),(2,3),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => 1 = 2 - 1
([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => ([],5)
 => ([],1)
 => ? = 1 - 1
([],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ? = 2 - 1
([(3,4),(3,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(3,5),(4,5)],6)
 => ? = 2 - 1
([(2,3),(2,4),(2,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,5),(3,5),(4,5)],6)
 => ? = 2 - 1
([(1,2),(1,3),(1,4),(1,5)],6)
 => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 2 - 1
([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
 => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 2 - 1
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ? = 2 - 1
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
 => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
 => ? = 2 - 1
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
 => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ? = 2 - 1
([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(4,5)],6)
 => ? = 2 - 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ? = 2 - 1
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 2 - 1
([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ? = 2 - 1
([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 2 - 1
([(1,4),(1,5),(5,2),(5,3)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(4,5)],6)
 => ? = 2 - 1
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
 => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
 => ? = 2 - 1
([(1,3),(1,4),(3,5),(4,2),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(3,5),(4,5)],6)
 => ? = 2 - 1
([(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 2 - 1
([(0,3),(0,4),(3,5),(4,1),(4,5),(5,2)],6)
 => ([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
 => ? = 2 - 1
([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6)
 => ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ? = 2 - 1
([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
 => ([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 2 - 1
([(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(3,5),(4,5)],6)
 => ? = 2 - 1
([(1,5),(2,5),(5,3),(5,4)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 2 - 1
([(0,5),(1,5),(5,2),(5,3),(5,4)],6)
 => ([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 2 - 1
([(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,5),(3,5),(4,5)],6)
 => ? = 2 - 1
([(0,5),(1,5),(2,5),(5,3),(5,4)],6)
 => ([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 2 - 1
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 2 - 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 2 - 1
([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
 => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
 => ? = 2 - 1
([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,5),(3,4)],6)
 => ? = 2 - 1
([(0,5),(1,4),(2,4),(2,5),(5,3)],6)
 => ([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)
 => ([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(3,4),(3,5)],6)
 => ? = 2 - 1
([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ? = 2 - 1
([(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(4,5)],6)
 => ? = 2 - 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ? = 2 - 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
 => ([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 2 - 1
([(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(4,5)],6)
 => ? = 2 - 1
([(1,5),(2,5),(3,4),(3,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,5),(3,4)],6)
 => ? = 2 - 1
([(0,5),(1,5),(2,3),(2,4)],6)
 => ([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(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)],6)
 => ? = 2 - 1
([(0,3),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(3,5),(4,5)],6)
 => ? = 2 - 1
([(0,5),(1,2),(1,4),(3,5),(4,3)],6)
 => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ? = 2 - 1
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ? = 2 - 1
([(0,5),(1,4),(3,5),(4,2),(4,3)],6)
 => ([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,4),(3,4),(3,5)],6)
 => ? = 2 - 1
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(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)],6)
 => ? = 2 - 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ? = 2 - 1
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ? = 2 - 1
([(2,5),(3,4),(3,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,5),(3,4)],6)
 => ? = 2 - 1
Description
The maximum magnitude of the Möbius function of a poset. The '''Möbius function''' of a poset is the multiplicative inverse of the zeta function in the incidence algebra. The Möbius value μ(x,y) is equal to the signed sum of chains from x to y, where odd-length chains are counted with a minus sign, so this statistic is bounded above by the total number of chains in the poset.
Matching statistic: St001578
Mapping
Mp00198: Posets —incomparability graph⟶ Graphs
Mp00156: Graphs —line graph⟶ Graphs
St001578: Graphs ⟶ ℤResult quality: 26% ●values known / values provided: 26%●distinct values known / distinct values provided: 33%
Values
([],1)
 => ([],1)
 => ([],0)
 => ? = 1 - 2
([],2)
 => ([(0,1)],2)
 => ([],1)
 => 0 = 2 - 2
([(0,1)],2)
 => ([],2)
 => ([],0)
 => ? = 1 - 2
([],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 0 = 2 - 2
([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 0 = 2 - 2
([(0,1),(0,2)],3)
 => ([(1,2)],3)
 => ([],1)
 => 0 = 2 - 2
([(0,2),(2,1)],3)
 => ([],3)
 => ([],0)
 => ? = 1 - 2
([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => ([],1)
 => 0 = 2 - 2
([],4)
 => ([(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 = 2 - 2
([(2,3)],4)
 => ([(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)
 => 0 = 2 - 2
([(1,2),(1,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 0 = 2 - 2
([(0,1),(0,2),(0,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 0 = 2 - 2
([(0,2),(0,3),(3,1)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 0 = 2 - 2
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ([],1)
 => 0 = 2 - 2
([(1,2),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 0 = 2 - 2
([(0,3),(3,1),(3,2)],4)
 => ([(2,3)],4)
 => ([],1)
 => 0 = 2 - 2
([(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 0 = 2 - 2
([(0,3),(1,3),(3,2)],4)
 => ([(2,3)],4)
 => ([],1)
 => 0 = 2 - 2
([(0,3),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 0 = 2 - 2
([(0,3),(1,2)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 0 = 2 - 2
([(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,2),(1,2)],3)
 => 0 = 2 - 2
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2)],4)
 => ([],2)
 => 0 = 2 - 2
([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ([],0)
 => ? = 1 - 2
([(0,3),(1,2),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 0 = 2 - 2
([],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(1,3),(1,6),(1,7),(1,8),(1,9),(2,3),(2,4),(2,5),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(4,9),(5,6),(5,8),(6,7),(6,8),(7,9),(8,9)],10)
 => ? = 2 - 2
([(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,4),(0,5),(0,7),(0,8),(1,2),(1,3),(1,7),(1,8),(2,3),(2,5),(2,6),(2,8),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,8),(6,7),(6,8),(7,8)],9)
 => ? = 2 - 2
([(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,5),(1,6),(1,7),(2,3),(2,4),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2 - 2
([(1,2),(1,3),(1,4)],5)
 => ([(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)
 => ? = 2 - 2
([(0,1),(0,2),(0,3),(0,4)],5)
 => ([(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 = 2 - 2
([(0,2),(0,3),(0,4),(4,1)],5)
 => ([(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)
 => 0 = 2 - 2
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 0 = 2 - 2
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 0 = 2 - 2
([(1,3),(1,4),(4,2)],5)
 => ([(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)
 => 0 = 2 - 2
([(0,3),(0,4),(4,1),(4,2)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 0 = 2 - 2
([(1,2),(1,3),(2,4),(3,4)],5)
 => ([(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)
 => 0 = 2 - 2
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(3,4)],5)
 => ([],1)
 => 0 = 2 - 2
([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 0 = 2 - 2
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => 0 = 2 - 2
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,4),(2,3)],5)
 => ([],2)
 => 0 = 2 - 2
([(2,3),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ? = 2 - 2
([(1,4),(4,2),(4,3)],5)
 => ([(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)
 => 0 = 2 - 2
([(0,4),(4,1),(4,2),(4,3)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 0 = 2 - 2
([(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,5),(1,6),(1,7),(2,3),(2,4),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2 - 2
([(1,4),(2,4),(4,3)],5)
 => ([(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)
 => 0 = 2 - 2
([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(1,4),(2,3)],5)
 => ([],2)
 => 0 = 2 - 2
([(1,4),(2,4),(3,4)],5)
 => ([(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)
 => ? = 2 - 2
([(0,4),(1,4),(2,4),(4,3)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 0 = 2 - 2
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(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 = 2 - 2
([(0,4),(1,4),(2,3)],5)
 => ([(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)
 => ? = 2 - 2
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(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 = 2 - 2
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(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 = 2 - 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => 0 = 2 - 2
([(0,4),(1,4),(2,3),(4,2)],5)
 => ([(3,4)],5)
 => ([],1)
 => 0 = 2 - 2
([(0,4),(1,3),(2,3),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 0 = 2 - 2
([(0,4),(1,4),(2,3),(2,4)],5)
 => ([(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 = 2 - 2
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(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)
 => 0 = 2 - 2
([(1,4),(2,3)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(2,5),(2,7),(3,4),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2 - 2
([(1,4),(2,3),(2,4)],5)
 => ([(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)
 => ? = 2 - 2
([(0,4),(1,2),(1,4),(2,3)],5)
 => ([(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 = 2 - 2
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => 0 = 2 - 2
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(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 = 2 - 2
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
 => ([(0,1),(2,4),(3,4)],5)
 => ([(1,2)],3)
 => 0 = 2 - 2
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
 => ([(1,4),(2,3)],5)
 => ([],2)
 => 0 = 2 - 2
([(0,4),(1,2),(1,4),(4,3)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 0 = 2 - 2
([(0,4),(1,2),(1,3)],5)
 => ([(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)
 => ? = 2 - 2
([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => ([],0)
 => ? = 1 - 2
([],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ?
 => ? = 2 - 2
([(4,5)],6)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ?
 => ? = 2 - 2
([(3,4),(3,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ?
 => ? = 2 - 2
([(2,3),(2,4),(2,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ?
 => ? = 2 - 2
([(1,2),(1,3),(1,4),(1,5)],6)
 => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ?
 => ? = 2 - 2
([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
 => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(1,3),(1,6),(1,7),(1,8),(1,9),(2,3),(2,4),(2,5),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(4,9),(5,6),(5,8),(6,7),(6,8),(7,9),(8,9)],10)
 => ? = 2 - 2
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
 => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,4),(0,5),(0,7),(0,8),(1,2),(1,3),(1,7),(1,8),(2,3),(2,5),(2,6),(2,8),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,8),(6,7),(6,8),(7,8)],9)
 => ? = 2 - 2
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,5),(1,6),(1,7),(2,3),(2,4),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2 - 2
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
 => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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)
 => ? = 2 - 2
([(1,3),(1,4),(1,5),(5,2)],6)
 => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,6),(0,7),(0,8),(0,9),(1,2),(1,4),(1,5),(1,7),(1,9),(2,3),(2,5),(2,7),(2,8),(3,4),(3,5),(3,6),(3,8),(4,5),(4,6),(4,9),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
 => ? = 2 - 2
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
 => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,5),(1,6),(1,7),(2,3),(2,4),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2 - 2
([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,6),(0,7),(0,8),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,8),(3,6),(3,7),(3,8),(4,5),(4,7),(4,8),(5,6),(5,8),(6,7),(6,8),(7,8)],9)
 => ? = 2 - 2
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,6),(0,7),(1,2),(1,5),(1,7),(2,5),(2,6),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2 - 2
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
 => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(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)
 => ? = 2 - 2
([(0,3),(0,4),(0,5),(4,2),(5,1)],6)
 => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,2),(0,3),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(2,5),(2,7),(3,4),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2 - 2
([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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)
 => ? = 2 - 2
([(2,3),(2,4),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ?
 => ? = 2 - 2
([(1,4),(1,5),(5,2),(5,3)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,6),(0,7),(0,8),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,8),(3,6),(3,7),(3,8),(4,5),(4,7),(4,8),(5,6),(5,8),(6,7),(6,8),(7,8)],9)
 => ? = 2 - 2
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
 => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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)
 => ? = 2 - 2
([(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(0,6),(0,7),(0,8),(1,3),(1,4),(1,7),(1,8),(1,9),(2,3),(2,4),(2,5),(2,6),(2,9),(3,5),(3,6),(3,9),(4,7),(4,8),(4,9),(5,6),(5,8),(5,9),(6,7),(6,9),(7,8),(7,9),(8,9)],10)
 => ? = 2 - 2
([(1,4),(1,5),(4,3),(5,2)],6)
 => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,2),(0,3),(0,7),(0,8),(1,2),(1,3),(1,5),(1,6),(2,6),(2,8),(3,5),(3,7),(4,5),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
 => ? = 2 - 2
([(1,3),(1,4),(3,5),(4,2),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(0,5),(0,7),(1,2),(1,4),(1,6),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2 - 2
([(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2 - 2
([(0,4),(0,5),(4,3),(5,1),(5,2)],6)
 => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(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)
 => ? = 2 - 2
([(3,4),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ?
 => ? = 2 - 2
([(2,3),(3,4),(3,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(0,6),(0,7),(0,8),(1,3),(1,4),(1,7),(1,8),(1,9),(2,3),(2,4),(2,5),(2,6),(2,9),(3,5),(3,6),(3,9),(4,7),(4,8),(4,9),(5,6),(5,8),(5,9),(6,7),(6,9),(7,8),(7,9),(8,9)],10)
 => ? = 2 - 2
([(1,5),(5,2),(5,3),(5,4)],6)
 => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,6),(0,7),(1,2),(1,5),(1,7),(2,5),(2,6),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2 - 2
([(2,3),(3,5),(5,4)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(0,6),(0,7),(0,8),(1,2),(1,3),(1,6),(1,7),(1,8),(2,3),(2,5),(2,7),(2,8),(3,4),(3,7),(3,8),(4,5),(4,6),(4,8),(5,6),(5,8),(6,8),(7,8)],9)
 => ? = 2 - 2
([(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ?
 => ? = 2 - 2
([(2,5),(3,5),(5,4)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(0,6),(0,7),(0,8),(1,3),(1,4),(1,7),(1,8),(1,9),(2,3),(2,4),(2,5),(2,6),(2,9),(3,5),(3,6),(3,9),(4,7),(4,8),(4,9),(5,6),(5,8),(5,9),(6,7),(6,9),(7,8),(7,9),(8,9)],10)
 => ? = 2 - 2
([(1,5),(2,5),(5,3),(5,4)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2 - 2
([(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ?
 => ? = 2 - 2
([(1,5),(2,5),(3,5),(5,4)],6)
 => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,6),(0,7),(1,2),(1,5),(1,7),(2,5),(2,6),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2 - 2
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ?
 => ? = 2 - 2
Description
The minimal number of edges to add or remove to make a graph a line graph.
Matching statistic: St000781
Mapping
Mp00074: Posets —to graph⟶ Graphs
Mp00037: Graphs —to partition of connected components⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000781: Integer partitions ⟶ ℤResult quality: 24% ●values known / values provided: 24%●distinct values known / distinct values provided: 33%
Values
([],1)
 => ([],1)
 => [1]
 => []
 => ? = 1 - 1
([],2)
 => ([],2)
 => [1,1]
 => [1]
 => 1 = 2 - 1
([(0,1)],2)
 => ([(0,1)],2)
 => [2]
 => []
 => ? = 1 - 1
([],3)
 => ([],3)
 => [1,1,1]
 => [1,1]
 => 1 = 2 - 1
([(1,2)],3)
 => ([(1,2)],3)
 => [2,1]
 => [1]
 => 1 = 2 - 1
([(0,1),(0,2)],3)
 => ([(0,2),(1,2)],3)
 => [3]
 => []
 => ? = 2 - 1
([(0,2),(2,1)],3)
 => ([(0,2),(1,2)],3)
 => [3]
 => []
 => ? = 1 - 1
([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => [3]
 => []
 => ? = 2 - 1
([],4)
 => ([],4)
 => [1,1,1,1]
 => [1,1,1]
 => 1 = 2 - 1
([(2,3)],4)
 => ([(2,3)],4)
 => [2,1,1]
 => [1,1]
 => 1 = 2 - 1
([(1,2),(1,3)],4)
 => ([(1,3),(2,3)],4)
 => [3,1]
 => [1]
 => 1 = 2 - 1
([(0,1),(0,2),(0,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => [4]
 => []
 => ? = 2 - 1
([(0,2),(0,3),(3,1)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => [4]
 => []
 => ? = 2 - 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => [4]
 => []
 => ? = 2 - 1
([(1,2),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => [3,1]
 => [1]
 => 1 = 2 - 1
([(0,3),(3,1),(3,2)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => [4]
 => []
 => ? = 2 - 1
([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => [3,1]
 => [1]
 => 1 = 2 - 1
([(0,3),(1,3),(3,2)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => [4]
 => []
 => ? = 2 - 1
([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => [4]
 => []
 => ? = 2 - 1
([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => [2,2]
 => [2]
 => 1 = 2 - 1
([(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => [4]
 => []
 => ? = 2 - 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => [4]
 => []
 => ? = 2 - 1
([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => [4]
 => []
 => ? = 1 - 1
([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => [4]
 => []
 => ? = 2 - 1
([],5)
 => ([],5)
 => [1,1,1,1,1]
 => [1,1,1,1]
 => 1 = 2 - 1
([(3,4)],5)
 => ([(3,4)],5)
 => [2,1,1,1]
 => [1,1,1]
 => 1 = 2 - 1
([(2,3),(2,4)],5)
 => ([(2,4),(3,4)],5)
 => [3,1,1]
 => [1,1]
 => 1 = 2 - 1
([(1,2),(1,3),(1,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => [4,1]
 => [1]
 => 1 = 2 - 1
([(0,1),(0,2),(0,3),(0,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,2),(0,3),(0,4),(4,1)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(1,3),(1,4),(4,2)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => [4,1]
 => [1]
 => 1 = 2 - 1
([(0,3),(0,4),(4,1),(4,2)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(1,2),(1,3),(2,4),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => [4,1]
 => [1]
 => 1 = 2 - 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(2,3),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => [3,1,1]
 => [1,1]
 => 1 = 2 - 1
([(1,4),(4,2),(4,3)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => [4,1]
 => [1]
 => 1 = 2 - 1
([(0,4),(4,1),(4,2),(4,3)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => [3,1,1]
 => [1,1]
 => 1 = 2 - 1
([(1,4),(2,4),(4,3)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => [4,1]
 => [1]
 => 1 = 2 - 1
([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => [4,1]
 => [1]
 => 1 = 2 - 1
([(0,4),(1,4),(2,4),(4,3)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,4),(1,4),(2,3)],5)
 => ([(0,1),(2,4),(3,4)],5)
 => [3,2]
 => [2]
 => 1 = 2 - 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,4),(1,4),(2,3),(4,2)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,4),(1,3),(2,3),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,4),(1,4),(2,3),(2,4)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(1,4),(2,3)],5)
 => ([(1,4),(2,3)],5)
 => [2,2,1]
 => [2,1]
 => 1 = 2 - 1
([(1,4),(2,3),(2,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => [4,1]
 => [1]
 => 1 = 2 - 1
([(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => [4,1]
 => [1]
 => 1 = 2 - 1
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,4),(1,2),(1,4),(4,3)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,4),(1,2),(1,3)],5)
 => ([(0,1),(2,4),(3,4)],5)
 => [3,2]
 => [2]
 => 1 = 2 - 1
([(0,4),(1,2),(1,3),(1,4)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,2),(0,4),(3,1),(4,3)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,4),(1,2),(1,3),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,3),(0,4),(1,2),(1,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,3),(1,2),(1,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(1,4),(3,2),(4,3)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => [4,1]
 => [1]
 => 1 = 2 - 1
([(1,4),(2,3),(3,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => [4,1]
 => [1]
 => 1 = 2 - 1
([(0,3),(1,4),(4,2)],5)
 => ([(0,1),(2,4),(3,4)],5)
 => [3,2]
 => [2]
 => 1 = 2 - 1
([],6)
 => ([],6)
 => [1,1,1,1,1,1]
 => [1,1,1,1,1]
 => 1 = 2 - 1
([(4,5)],6)
 => ([(4,5)],6)
 => [2,1,1,1,1]
 => [1,1,1,1]
 => 1 = 2 - 1
([(3,4),(3,5)],6)
 => ([(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => 1 = 2 - 1
([(2,3),(2,4),(2,5)],6)
 => ([(2,5),(3,5),(4,5)],6)
 => [4,1,1]
 => [1,1]
 => 1 = 2 - 1
([(1,2),(1,3),(1,4),(1,5)],6)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => 1 = 2 - 1
([(1,3),(1,4),(1,5),(5,2)],6)
 => ([(1,5),(2,5),(3,4),(4,5)],6)
 => [5,1]
 => [1]
 => 1 = 2 - 1
([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
 => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => 1 = 2 - 1
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [5,1]
 => [1]
 => 1 = 2 - 1
([(2,3),(2,4),(4,5)],6)
 => ([(2,5),(3,4),(4,5)],6)
 => [4,1,1]
 => [1,1]
 => 1 = 2 - 1
([(1,4),(1,5),(5,2),(5,3)],6)
 => ([(1,5),(2,5),(3,4),(4,5)],6)
 => [5,1]
 => [1]
 => 1 = 2 - 1
([(2,3),(2,4),(3,5),(4,5)],6)
 => ([(2,4),(2,5),(3,4),(3,5)],6)
 => [4,1,1]
 => [1,1]
 => 1 = 2 - 1
([(1,2),(1,3),(2,5),(3,5),(5,4)],6)
 => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => 1 = 2 - 1
([(1,4),(1,5),(4,3),(5,2)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => [5,1]
 => [1]
 => 1 = 2 - 1
([(1,3),(1,4),(3,5),(4,2),(4,5)],6)
 => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => 1 = 2 - 1
([(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [5,1]
 => [1]
 => 1 = 2 - 1
([(3,4),(4,5)],6)
 => ([(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => 1 = 2 - 1
([(2,3),(3,4),(3,5)],6)
 => ([(2,5),(3,5),(4,5)],6)
 => [4,1,1]
 => [1,1]
 => 1 = 2 - 1
([(1,5),(5,2),(5,3),(5,4)],6)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => 1 = 2 - 1
([(2,3),(3,5),(5,4)],6)
 => ([(2,5),(3,4),(4,5)],6)
 => [4,1,1]
 => [1,1]
 => 1 = 2 - 1
([(1,4),(4,5),(5,2),(5,3)],6)
 => ([(1,5),(2,5),(3,4),(4,5)],6)
 => [5,1]
 => [1]
 => 1 = 2 - 1
([(3,5),(4,5)],6)
 => ([(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => 1 = 2 - 1
([(2,5),(3,5),(5,4)],6)
 => ([(2,5),(3,5),(4,5)],6)
 => [4,1,1]
 => [1,1]
 => 1 = 2 - 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: St001901
Mapping
Mp00074: Posets —to graph⟶ Graphs
Mp00037: Graphs —to partition of connected components⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001901: Integer partitions ⟶ ℤResult quality: 24% ●values known / values provided: 24%●distinct values known / distinct values provided: 33%
Values
([],1)
 => ([],1)
 => [1]
 => []
 => ? = 1 - 1
([],2)
 => ([],2)
 => [1,1]
 => [1]
 => 1 = 2 - 1
([(0,1)],2)
 => ([(0,1)],2)
 => [2]
 => []
 => ? = 1 - 1
([],3)
 => ([],3)
 => [1,1,1]
 => [1,1]
 => 1 = 2 - 1
([(1,2)],3)
 => ([(1,2)],3)
 => [2,1]
 => [1]
 => 1 = 2 - 1
([(0,1),(0,2)],3)
 => ([(0,2),(1,2)],3)
 => [3]
 => []
 => ? = 2 - 1
([(0,2),(2,1)],3)
 => ([(0,2),(1,2)],3)
 => [3]
 => []
 => ? = 1 - 1
([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => [3]
 => []
 => ? = 2 - 1
([],4)
 => ([],4)
 => [1,1,1,1]
 => [1,1,1]
 => 1 = 2 - 1
([(2,3)],4)
 => ([(2,3)],4)
 => [2,1,1]
 => [1,1]
 => 1 = 2 - 1
([(1,2),(1,3)],4)
 => ([(1,3),(2,3)],4)
 => [3,1]
 => [1]
 => 1 = 2 - 1
([(0,1),(0,2),(0,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => [4]
 => []
 => ? = 2 - 1
([(0,2),(0,3),(3,1)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => [4]
 => []
 => ? = 2 - 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => [4]
 => []
 => ? = 2 - 1
([(1,2),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => [3,1]
 => [1]
 => 1 = 2 - 1
([(0,3),(3,1),(3,2)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => [4]
 => []
 => ? = 2 - 1
([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => [3,1]
 => [1]
 => 1 = 2 - 1
([(0,3),(1,3),(3,2)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => [4]
 => []
 => ? = 2 - 1
([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => [4]
 => []
 => ? = 2 - 1
([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => [2,2]
 => [2]
 => 1 = 2 - 1
([(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => [4]
 => []
 => ? = 2 - 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => [4]
 => []
 => ? = 2 - 1
([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => [4]
 => []
 => ? = 1 - 1
([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => [4]
 => []
 => ? = 2 - 1
([],5)
 => ([],5)
 => [1,1,1,1,1]
 => [1,1,1,1]
 => 1 = 2 - 1
([(3,4)],5)
 => ([(3,4)],5)
 => [2,1,1,1]
 => [1,1,1]
 => 1 = 2 - 1
([(2,3),(2,4)],5)
 => ([(2,4),(3,4)],5)
 => [3,1,1]
 => [1,1]
 => 1 = 2 - 1
([(1,2),(1,3),(1,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => [4,1]
 => [1]
 => 1 = 2 - 1
([(0,1),(0,2),(0,3),(0,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,2),(0,3),(0,4),(4,1)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(1,3),(1,4),(4,2)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => [4,1]
 => [1]
 => 1 = 2 - 1
([(0,3),(0,4),(4,1),(4,2)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(1,2),(1,3),(2,4),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => [4,1]
 => [1]
 => 1 = 2 - 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(2,3),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => [3,1,1]
 => [1,1]
 => 1 = 2 - 1
([(1,4),(4,2),(4,3)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => [4,1]
 => [1]
 => 1 = 2 - 1
([(0,4),(4,1),(4,2),(4,3)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => [3,1,1]
 => [1,1]
 => 1 = 2 - 1
([(1,4),(2,4),(4,3)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => [4,1]
 => [1]
 => 1 = 2 - 1
([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => [4,1]
 => [1]
 => 1 = 2 - 1
([(0,4),(1,4),(2,4),(4,3)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,4),(1,4),(2,3)],5)
 => ([(0,1),(2,4),(3,4)],5)
 => [3,2]
 => [2]
 => 1 = 2 - 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,4),(1,4),(2,3),(4,2)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,4),(1,3),(2,3),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,4),(1,4),(2,3),(2,4)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(1,4),(2,3)],5)
 => ([(1,4),(2,3)],5)
 => [2,2,1]
 => [2,1]
 => 1 = 2 - 1
([(1,4),(2,3),(2,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => [4,1]
 => [1]
 => 1 = 2 - 1
([(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => [4,1]
 => [1]
 => 1 = 2 - 1
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,4),(1,2),(1,4),(4,3)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,4),(1,2),(1,3)],5)
 => ([(0,1),(2,4),(3,4)],5)
 => [3,2]
 => [2]
 => 1 = 2 - 1
([(0,4),(1,2),(1,3),(1,4)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,2),(0,4),(3,1),(4,3)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,4),(1,2),(1,3),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,3),(0,4),(1,2),(1,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,3),(1,2),(1,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(1,4),(3,2),(4,3)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => [4,1]
 => [1]
 => 1 = 2 - 1
([(1,4),(2,3),(3,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => [4,1]
 => [1]
 => 1 = 2 - 1
([(0,3),(1,4),(4,2)],5)
 => ([(0,1),(2,4),(3,4)],5)
 => [3,2]
 => [2]
 => 1 = 2 - 1
([],6)
 => ([],6)
 => [1,1,1,1,1,1]
 => [1,1,1,1,1]
 => 1 = 2 - 1
([(4,5)],6)
 => ([(4,5)],6)
 => [2,1,1,1,1]
 => [1,1,1,1]
 => 1 = 2 - 1
([(3,4),(3,5)],6)
 => ([(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => 1 = 2 - 1
([(2,3),(2,4),(2,5)],6)
 => ([(2,5),(3,5),(4,5)],6)
 => [4,1,1]
 => [1,1]
 => 1 = 2 - 1
([(1,2),(1,3),(1,4),(1,5)],6)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => 1 = 2 - 1
([(1,3),(1,4),(1,5),(5,2)],6)
 => ([(1,5),(2,5),(3,4),(4,5)],6)
 => [5,1]
 => [1]
 => 1 = 2 - 1
([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
 => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => 1 = 2 - 1
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [5,1]
 => [1]
 => 1 = 2 - 1
([(2,3),(2,4),(4,5)],6)
 => ([(2,5),(3,4),(4,5)],6)
 => [4,1,1]
 => [1,1]
 => 1 = 2 - 1
([(1,4),(1,5),(5,2),(5,3)],6)
 => ([(1,5),(2,5),(3,4),(4,5)],6)
 => [5,1]
 => [1]
 => 1 = 2 - 1
([(2,3),(2,4),(3,5),(4,5)],6)
 => ([(2,4),(2,5),(3,4),(3,5)],6)
 => [4,1,1]
 => [1,1]
 => 1 = 2 - 1
([(1,2),(1,3),(2,5),(3,5),(5,4)],6)
 => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => 1 = 2 - 1
([(1,4),(1,5),(4,3),(5,2)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => [5,1]
 => [1]
 => 1 = 2 - 1
([(1,3),(1,4),(3,5),(4,2),(4,5)],6)
 => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => 1 = 2 - 1
([(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [5,1]
 => [1]
 => 1 = 2 - 1
([(3,4),(4,5)],6)
 => ([(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => 1 = 2 - 1
([(2,3),(3,4),(3,5)],6)
 => ([(2,5),(3,5),(4,5)],6)
 => [4,1,1]
 => [1,1]
 => 1 = 2 - 1
([(1,5),(5,2),(5,3),(5,4)],6)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => 1 = 2 - 1
([(2,3),(3,5),(5,4)],6)
 => ([(2,5),(3,4),(4,5)],6)
 => [4,1,1]
 => [1,1]
 => 1 = 2 - 1
([(1,4),(4,5),(5,2),(5,3)],6)
 => ([(1,5),(2,5),(3,4),(4,5)],6)
 => [5,1]
 => [1]
 => 1 = 2 - 1
([(3,5),(4,5)],6)
 => ([(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => 1 = 2 - 1
([(2,5),(3,5),(5,4)],6)
 => ([(2,5),(3,5),(4,5)],6)
 => [4,1,1]
 => [1,1]
 => 1 = 2 - 1
Description
The largest multiplicity of an irreducible representation contained in the higher Lie character for an integer partition.
Matching statistic: St001283
Mapping
Mp00307: Posets —promotion cycle type⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001283: Integer partitions ⟶ ℤResult quality: 17% ●values known / values provided: 17%●distinct values known / distinct values provided: 33%
Values
([],1)
 => [1]
 => []
 => ? = 1 - 2
([],2)
 => [2]
 => []
 => ? = 2 - 2
([(0,1)],2)
 => [1]
 => []
 => ? = 1 - 2
([],3)
 => [3,3]
 => [3]
 => 0 = 2 - 2
([(1,2)],3)
 => [3]
 => []
 => ? = 2 - 2
([(0,1),(0,2)],3)
 => [2]
 => []
 => ? = 2 - 2
([(0,2),(2,1)],3)
 => [1]
 => []
 => ? = 1 - 2
([(0,2),(1,2)],3)
 => [2]
 => []
 => ? = 2 - 2
([],4)
 => [4,4,4,4,4,4]
 => [4,4,4,4,4]
 => ? = 2 - 2
([(2,3)],4)
 => [4,4,4]
 => [4,4]
 => 0 = 2 - 2
([(1,2),(1,3)],4)
 => [8]
 => []
 => ? = 2 - 2
([(0,1),(0,2),(0,3)],4)
 => [3,3]
 => [3]
 => 0 = 2 - 2
([(0,2),(0,3),(3,1)],4)
 => [3]
 => []
 => ? = 2 - 2
([(0,1),(0,2),(1,3),(2,3)],4)
 => [2]
 => []
 => ? = 2 - 2
([(1,2),(2,3)],4)
 => [4]
 => []
 => ? = 2 - 2
([(0,3),(3,1),(3,2)],4)
 => [2]
 => []
 => ? = 2 - 2
([(1,3),(2,3)],4)
 => [8]
 => []
 => ? = 2 - 2
([(0,3),(1,3),(3,2)],4)
 => [2]
 => []
 => ? = 2 - 2
([(0,3),(1,3),(2,3)],4)
 => [3,3]
 => [3]
 => 0 = 2 - 2
([(0,3),(1,2)],4)
 => [4,2]
 => [2]
 => 0 = 2 - 2
([(0,3),(1,2),(1,3)],4)
 => [3,2]
 => [2]
 => 0 = 2 - 2
([(0,2),(0,3),(1,2),(1,3)],4)
 => [2,2]
 => [2]
 => 0 = 2 - 2
([(0,3),(2,1),(3,2)],4)
 => [1]
 => []
 => ? = 1 - 2
([(0,3),(1,2),(2,3)],4)
 => [3]
 => []
 => ? = 2 - 2
([],5)
 => [5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5]
 => [5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5]
 => ? = 2 - 2
([(3,4)],5)
 => [5,5,5,5,5,5,5,5,5,5,5,5]
 => [5,5,5,5,5,5,5,5,5,5,5]
 => ? = 2 - 2
([(2,3),(2,4)],5)
 => [10,10,10,10]
 => [10,10,10]
 => ? = 2 - 2
([(1,2),(1,3),(1,4)],5)
 => [15,15]
 => [15]
 => 0 = 2 - 2
([(0,1),(0,2),(0,3),(0,4)],5)
 => [4,4,4,4,4,4]
 => [4,4,4,4,4]
 => ? = 2 - 2
([(0,2),(0,3),(0,4),(4,1)],5)
 => [4,4,4]
 => [4,4]
 => 0 = 2 - 2
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => [8]
 => []
 => ? = 2 - 2
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => [3,3]
 => [3]
 => 0 = 2 - 2
([(1,3),(1,4),(4,2)],5)
 => [15]
 => []
 => ? = 2 - 2
([(0,3),(0,4),(4,1),(4,2)],5)
 => [8]
 => []
 => ? = 2 - 2
([(1,2),(1,3),(2,4),(3,4)],5)
 => [5,5]
 => [5]
 => 0 = 2 - 2
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => [2]
 => []
 => ? = 2 - 2
([(0,3),(0,4),(3,2),(4,1)],5)
 => [4,2]
 => [2]
 => 0 = 2 - 2
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => [3,2]
 => [2]
 => 0 = 2 - 2
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => [2,2]
 => [2]
 => 0 = 2 - 2
([(2,3),(3,4)],5)
 => [5,5,5,5]
 => [5,5,5]
 => 0 = 2 - 2
([(1,4),(4,2),(4,3)],5)
 => [5,5]
 => [5]
 => 0 = 2 - 2
([(0,4),(4,1),(4,2),(4,3)],5)
 => [3,3]
 => [3]
 => 0 = 2 - 2
([(2,4),(3,4)],5)
 => [10,10,10,10]
 => [10,10,10]
 => ? = 2 - 2
([(1,4),(2,4),(4,3)],5)
 => [5,5]
 => [5]
 => 0 = 2 - 2
([(0,4),(1,4),(4,2),(4,3)],5)
 => [2,2]
 => [2]
 => 0 = 2 - 2
([(1,4),(2,4),(3,4)],5)
 => [15,15]
 => [15]
 => 0 = 2 - 2
([(0,4),(1,4),(2,4),(4,3)],5)
 => [3,3]
 => [3]
 => 0 = 2 - 2
([(0,4),(1,4),(2,4),(3,4)],5)
 => [4,4,4,4,4,4]
 => [4,4,4,4,4]
 => ? = 2 - 2
([(0,4),(1,4),(2,3)],5)
 => [10,10]
 => [10]
 => 0 = 2 - 2
([(0,4),(1,3),(2,3),(2,4)],5)
 => [12,4]
 => [4]
 => 0 = 2 - 2
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [14]
 => []
 => ? = 2 - 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [6,6]
 => [6]
 => 0 = 2 - 2
([(0,4),(1,4),(2,3),(4,2)],5)
 => [2]
 => []
 => ? = 2 - 2
([(0,4),(1,3),(2,3),(3,4)],5)
 => [8]
 => []
 => ? = 2 - 2
([(0,4),(1,4),(2,3),(2,4)],5)
 => [10,4,4]
 => [4,4]
 => 0 = 2 - 2
([(0,4),(1,4),(2,3),(3,4)],5)
 => [4,4,4]
 => [4,4]
 => 0 = 2 - 2
([(1,4),(2,3)],5)
 => [5,5,5,5,5,5]
 => [5,5,5,5,5]
 => ? = 2 - 2
([(1,4),(2,3),(2,4)],5)
 => [15,5,5]
 => [5,5]
 => 0 = 2 - 2
([(0,4),(1,2),(1,4),(2,3)],5)
 => [5,4]
 => [4]
 => 0 = 2 - 2
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
 => [3,2]
 => [2]
 => 0 = 2 - 2
([(1,3),(1,4),(2,3),(2,4)],5)
 => [5,5,5,5]
 => [5,5,5]
 => 0 = 2 - 2
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
 => [6]
 => []
 => ? = 2 - 2
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
 => [2,2]
 => [2]
 => 0 = 2 - 2
([(0,4),(1,2),(1,4),(4,3)],5)
 => [7]
 => []
 => ? = 2 - 2
([(0,4),(1,2),(1,3)],5)
 => [10,10]
 => [10]
 => 0 = 2 - 2
([(0,4),(1,2),(1,3),(1,4)],5)
 => [10,4,4]
 => [4,4]
 => 0 = 2 - 2
([(0,2),(0,4),(3,1),(4,3)],5)
 => [4]
 => []
 => ? = 2 - 2
([(0,4),(1,2),(1,3),(3,4)],5)
 => [4,4,3]
 => [4,3]
 => 0 = 2 - 2
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => [3]
 => []
 => ? = 2 - 2
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [8]
 => []
 => ? = 2 - 2
([(0,3),(0,4),(1,2),(1,4)],5)
 => [12,4]
 => [4]
 => 0 = 2 - 2
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => [14]
 => []
 => ? = 2 - 2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => [6,6]
 => [6]
 => 0 = 2 - 2
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
 => [5,3]
 => [3]
 => 0 = 2 - 2
([(0,3),(1,2),(1,4),(3,4)],5)
 => [5,4]
 => [4]
 => 0 = 2 - 2
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
 => [6]
 => []
 => ? = 2 - 2
([(1,4),(3,2),(4,3)],5)
 => [5]
 => []
 => ? = 2 - 2
([(0,3),(3,4),(4,1),(4,2)],5)
 => [2]
 => []
 => ? = 2 - 2
([(1,4),(2,3),(3,4)],5)
 => [15]
 => []
 => ? = 2 - 2
([(0,4),(1,2),(2,4),(4,3)],5)
 => [3]
 => []
 => ? = 2 - 2
([(0,3),(1,4),(4,2)],5)
 => [5,5]
 => [5]
 => 0 = 2 - 2
([(0,4),(3,2),(4,1),(4,3)],5)
 => [3]
 => []
 => ? = 2 - 2
([(0,4),(1,2),(2,3),(2,4)],5)
 => [7]
 => []
 => ? = 2 - 2
([(0,4),(2,3),(3,1),(4,2)],5)
 => [1]
 => []
 => ? = 1 - 2
([(0,3),(1,2),(2,4),(3,4)],5)
 => [4,2]
 => [2]
 => 0 = 2 - 2
([(0,4),(1,2),(2,3),(3,4)],5)
 => [4]
 => []
 => ? = 2 - 2
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => [2]
 => []
 => ? = 2 - 2
([],6)
 => [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]
 => ?
 => ? = 2 - 2
([(4,5)],6)
 => [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]
 => ?
 => ? = 2 - 2
([(3,4),(3,5)],6)
 => [12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12]
 => ?
 => ? = 2 - 2
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
 => [15,15]
 => [15]
 => 0 = 2 - 2
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => [3,3]
 => [3]
 => 0 = 2 - 2
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
 => [10,10]
 => [10]
 => 0 = 2 - 2
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6)
 => [12,4]
 => [4]
 => 0 = 2 - 2
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [6,6]
 => [6]
 => 0 = 2 - 2
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6)
 => [10,4,4]
 => [4,4]
 => 0 = 2 - 2
([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6)
 => [5,5]
 => [5]
 => 0 = 2 - 2
([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6)
 => [15,5,5]
 => [5,5]
 => 0 = 2 - 2
([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6)
 => [5,5,5,5]
 => [5,5,5]
 => 0 = 2 - 2
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
 => [15,15]
 => [15]
 => 0 = 2 - 2
Description
The number of finite solvable groups that are realised by the given partition over the complex numbers. A finite group G is ''realised'' by the partition (a1,…,am) if its group algebra over the complex numbers is isomorphic to the direct product of ai×ai matrix rings over the complex numbers. The smallest partition which does not realise a solvable group, but does realise a finite group, is (5,4,3,3,1).
Matching statistic: St001284
Mapping
Mp00307: Posets —promotion cycle type⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001284: Integer partitions ⟶ ℤResult quality: 17% ●values known / values provided: 17%●distinct values known / distinct values provided: 33%
Values
([],1)
 => [1]
 => []
 => ? = 1 - 2
([],2)
 => [2]
 => []
 => ? = 2 - 2
([(0,1)],2)
 => [1]
 => []
 => ? = 1 - 2
([],3)
 => [3,3]
 => [3]
 => 0 = 2 - 2
([(1,2)],3)
 => [3]
 => []
 => ? = 2 - 2
([(0,1),(0,2)],3)
 => [2]
 => []
 => ? = 2 - 2
([(0,2),(2,1)],3)
 => [1]
 => []
 => ? = 1 - 2
([(0,2),(1,2)],3)
 => [2]
 => []
 => ? = 2 - 2
([],4)
 => [4,4,4,4,4,4]
 => [4,4,4,4,4]
 => ? = 2 - 2
([(2,3)],4)
 => [4,4,4]
 => [4,4]
 => 0 = 2 - 2
([(1,2),(1,3)],4)
 => [8]
 => []
 => ? = 2 - 2
([(0,1),(0,2),(0,3)],4)
 => [3,3]
 => [3]
 => 0 = 2 - 2
([(0,2),(0,3),(3,1)],4)
 => [3]
 => []
 => ? = 2 - 2
([(0,1),(0,2),(1,3),(2,3)],4)
 => [2]
 => []
 => ? = 2 - 2
([(1,2),(2,3)],4)
 => [4]
 => []
 => ? = 2 - 2
([(0,3),(3,1),(3,2)],4)
 => [2]
 => []
 => ? = 2 - 2
([(1,3),(2,3)],4)
 => [8]
 => []
 => ? = 2 - 2
([(0,3),(1,3),(3,2)],4)
 => [2]
 => []
 => ? = 2 - 2
([(0,3),(1,3),(2,3)],4)
 => [3,3]
 => [3]
 => 0 = 2 - 2
([(0,3),(1,2)],4)
 => [4,2]
 => [2]
 => 0 = 2 - 2
([(0,3),(1,2),(1,3)],4)
 => [3,2]
 => [2]
 => 0 = 2 - 2
([(0,2),(0,3),(1,2),(1,3)],4)
 => [2,2]
 => [2]
 => 0 = 2 - 2
([(0,3),(2,1),(3,2)],4)
 => [1]
 => []
 => ? = 1 - 2
([(0,3),(1,2),(2,3)],4)
 => [3]
 => []
 => ? = 2 - 2
([],5)
 => [5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5]
 => [5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5]
 => ? = 2 - 2
([(3,4)],5)
 => [5,5,5,5,5,5,5,5,5,5,5,5]
 => [5,5,5,5,5,5,5,5,5,5,5]
 => ? = 2 - 2
([(2,3),(2,4)],5)
 => [10,10,10,10]
 => [10,10,10]
 => ? = 2 - 2
([(1,2),(1,3),(1,4)],5)
 => [15,15]
 => [15]
 => 0 = 2 - 2
([(0,1),(0,2),(0,3),(0,4)],5)
 => [4,4,4,4,4,4]
 => [4,4,4,4,4]
 => ? = 2 - 2
([(0,2),(0,3),(0,4),(4,1)],5)
 => [4,4,4]
 => [4,4]
 => 0 = 2 - 2
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => [8]
 => []
 => ? = 2 - 2
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => [3,3]
 => [3]
 => 0 = 2 - 2
([(1,3),(1,4),(4,2)],5)
 => [15]
 => []
 => ? = 2 - 2
([(0,3),(0,4),(4,1),(4,2)],5)
 => [8]
 => []
 => ? = 2 - 2
([(1,2),(1,3),(2,4),(3,4)],5)
 => [5,5]
 => [5]
 => 0 = 2 - 2
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => [2]
 => []
 => ? = 2 - 2
([(0,3),(0,4),(3,2),(4,1)],5)
 => [4,2]
 => [2]
 => 0 = 2 - 2
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => [3,2]
 => [2]
 => 0 = 2 - 2
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => [2,2]
 => [2]
 => 0 = 2 - 2
([(2,3),(3,4)],5)
 => [5,5,5,5]
 => [5,5,5]
 => 0 = 2 - 2
([(1,4),(4,2),(4,3)],5)
 => [5,5]
 => [5]
 => 0 = 2 - 2
([(0,4),(4,1),(4,2),(4,3)],5)
 => [3,3]
 => [3]
 => 0 = 2 - 2
([(2,4),(3,4)],5)
 => [10,10,10,10]
 => [10,10,10]
 => ? = 2 - 2
([(1,4),(2,4),(4,3)],5)
 => [5,5]
 => [5]
 => 0 = 2 - 2
([(0,4),(1,4),(4,2),(4,3)],5)
 => [2,2]
 => [2]
 => 0 = 2 - 2
([(1,4),(2,4),(3,4)],5)
 => [15,15]
 => [15]
 => 0 = 2 - 2
([(0,4),(1,4),(2,4),(4,3)],5)
 => [3,3]
 => [3]
 => 0 = 2 - 2
([(0,4),(1,4),(2,4),(3,4)],5)
 => [4,4,4,4,4,4]
 => [4,4,4,4,4]
 => ? = 2 - 2
([(0,4),(1,4),(2,3)],5)
 => [10,10]
 => [10]
 => 0 = 2 - 2
([(0,4),(1,3),(2,3),(2,4)],5)
 => [12,4]
 => [4]
 => 0 = 2 - 2
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [14]
 => []
 => ? = 2 - 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [6,6]
 => [6]
 => 0 = 2 - 2
([(0,4),(1,4),(2,3),(4,2)],5)
 => [2]
 => []
 => ? = 2 - 2
([(0,4),(1,3),(2,3),(3,4)],5)
 => [8]
 => []
 => ? = 2 - 2
([(0,4),(1,4),(2,3),(2,4)],5)
 => [10,4,4]
 => [4,4]
 => 0 = 2 - 2
([(0,4),(1,4),(2,3),(3,4)],5)
 => [4,4,4]
 => [4,4]
 => 0 = 2 - 2
([(1,4),(2,3)],5)
 => [5,5,5,5,5,5]
 => [5,5,5,5,5]
 => ? = 2 - 2
([(1,4),(2,3),(2,4)],5)
 => [15,5,5]
 => [5,5]
 => 0 = 2 - 2
([(0,4),(1,2),(1,4),(2,3)],5)
 => [5,4]
 => [4]
 => 0 = 2 - 2
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
 => [3,2]
 => [2]
 => 0 = 2 - 2
([(1,3),(1,4),(2,3),(2,4)],5)
 => [5,5,5,5]
 => [5,5,5]
 => 0 = 2 - 2
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
 => [6]
 => []
 => ? = 2 - 2
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
 => [2,2]
 => [2]
 => 0 = 2 - 2
([(0,4),(1,2),(1,4),(4,3)],5)
 => [7]
 => []
 => ? = 2 - 2
([(0,4),(1,2),(1,3)],5)
 => [10,10]
 => [10]
 => 0 = 2 - 2
([(0,4),(1,2),(1,3),(1,4)],5)
 => [10,4,4]
 => [4,4]
 => 0 = 2 - 2
([(0,2),(0,4),(3,1),(4,3)],5)
 => [4]
 => []
 => ? = 2 - 2
([(0,4),(1,2),(1,3),(3,4)],5)
 => [4,4,3]
 => [4,3]
 => 0 = 2 - 2
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => [3]
 => []
 => ? = 2 - 2
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [8]
 => []
 => ? = 2 - 2
([(0,3),(0,4),(1,2),(1,4)],5)
 => [12,4]
 => [4]
 => 0 = 2 - 2
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => [14]
 => []
 => ? = 2 - 2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => [6,6]
 => [6]
 => 0 = 2 - 2
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
 => [5,3]
 => [3]
 => 0 = 2 - 2
([(0,3),(1,2),(1,4),(3,4)],5)
 => [5,4]
 => [4]
 => 0 = 2 - 2
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
 => [6]
 => []
 => ? = 2 - 2
([(1,4),(3,2),(4,3)],5)
 => [5]
 => []
 => ? = 2 - 2
([(0,3),(3,4),(4,1),(4,2)],5)
 => [2]
 => []
 => ? = 2 - 2
([(1,4),(2,3),(3,4)],5)
 => [15]
 => []
 => ? = 2 - 2
([(0,4),(1,2),(2,4),(4,3)],5)
 => [3]
 => []
 => ? = 2 - 2
([(0,3),(1,4),(4,2)],5)
 => [5,5]
 => [5]
 => 0 = 2 - 2
([(0,4),(3,2),(4,1),(4,3)],5)
 => [3]
 => []
 => ? = 2 - 2
([(0,4),(1,2),(2,3),(2,4)],5)
 => [7]
 => []
 => ? = 2 - 2
([(0,4),(2,3),(3,1),(4,2)],5)
 => [1]
 => []
 => ? = 1 - 2
([(0,3),(1,2),(2,4),(3,4)],5)
 => [4,2]
 => [2]
 => 0 = 2 - 2
([(0,4),(1,2),(2,3),(3,4)],5)
 => [4]
 => []
 => ? = 2 - 2
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => [2]
 => []
 => ? = 2 - 2
([],6)
 => [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]
 => ?
 => ? = 2 - 2
([(4,5)],6)
 => [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]
 => ?
 => ? = 2 - 2
([(3,4),(3,5)],6)
 => [12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12]
 => ?
 => ? = 2 - 2
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
 => [15,15]
 => [15]
 => 0 = 2 - 2
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => [3,3]
 => [3]
 => 0 = 2 - 2
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
 => [10,10]
 => [10]
 => 0 = 2 - 2
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6)
 => [12,4]
 => [4]
 => 0 = 2 - 2
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [6,6]
 => [6]
 => 0 = 2 - 2
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6)
 => [10,4,4]
 => [4,4]
 => 0 = 2 - 2
([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6)
 => [5,5]
 => [5]
 => 0 = 2 - 2
([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6)
 => [15,5,5]
 => [5,5]
 => 0 = 2 - 2
([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6)
 => [5,5,5,5]
 => [5,5,5]
 => 0 = 2 - 2
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
 => [15,15]
 => [15]
 => 0 = 2 - 2
Description
The number of finite groups that are realised by the given partition over the complex numbers. A finite group G is 'realised' by the partition (a1,...,am) if its group algebra over the complex numbers is isomorphic to the direct product of ai×ai matrix rings over the complex numbers.
Matching statistic: St001785
Mapping
Mp00307: Posets —promotion cycle type⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001785: Integer partitions ⟶ ℤResult quality: 17% ●values known / values provided: 17%●distinct values known / distinct values provided: 33%
Values
([],1)
 => [1]
 => []
 => ? = 1 - 2
([],2)
 => [2]
 => []
 => ? = 2 - 2
([(0,1)],2)
 => [1]
 => []
 => ? = 1 - 2
([],3)
 => [3,3]
 => [3]
 => 0 = 2 - 2
([(1,2)],3)
 => [3]
 => []
 => ? = 2 - 2
([(0,1),(0,2)],3)
 => [2]
 => []
 => ? = 2 - 2
([(0,2),(2,1)],3)
 => [1]
 => []
 => ? = 1 - 2
([(0,2),(1,2)],3)
 => [2]
 => []
 => ? = 2 - 2
([],4)
 => [4,4,4,4,4,4]
 => [4,4,4,4,4]
 => ? = 2 - 2
([(2,3)],4)
 => [4,4,4]
 => [4,4]
 => 0 = 2 - 2
([(1,2),(1,3)],4)
 => [8]
 => []
 => ? = 2 - 2
([(0,1),(0,2),(0,3)],4)
 => [3,3]
 => [3]
 => 0 = 2 - 2
([(0,2),(0,3),(3,1)],4)
 => [3]
 => []
 => ? = 2 - 2
([(0,1),(0,2),(1,3),(2,3)],4)
 => [2]
 => []
 => ? = 2 - 2
([(1,2),(2,3)],4)
 => [4]
 => []
 => ? = 2 - 2
([(0,3),(3,1),(3,2)],4)
 => [2]
 => []
 => ? = 2 - 2
([(1,3),(2,3)],4)
 => [8]
 => []
 => ? = 2 - 2
([(0,3),(1,3),(3,2)],4)
 => [2]
 => []
 => ? = 2 - 2
([(0,3),(1,3),(2,3)],4)
 => [3,3]
 => [3]
 => 0 = 2 - 2
([(0,3),(1,2)],4)
 => [4,2]
 => [2]
 => 0 = 2 - 2
([(0,3),(1,2),(1,3)],4)
 => [3,2]
 => [2]
 => 0 = 2 - 2
([(0,2),(0,3),(1,2),(1,3)],4)
 => [2,2]
 => [2]
 => 0 = 2 - 2
([(0,3),(2,1),(3,2)],4)
 => [1]
 => []
 => ? = 1 - 2
([(0,3),(1,2),(2,3)],4)
 => [3]
 => []
 => ? = 2 - 2
([],5)
 => [5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5]
 => [5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5]
 => ? = 2 - 2
([(3,4)],5)
 => [5,5,5,5,5,5,5,5,5,5,5,5]
 => [5,5,5,5,5,5,5,5,5,5,5]
 => ? = 2 - 2
([(2,3),(2,4)],5)
 => [10,10,10,10]
 => [10,10,10]
 => ? = 2 - 2
([(1,2),(1,3),(1,4)],5)
 => [15,15]
 => [15]
 => 0 = 2 - 2
([(0,1),(0,2),(0,3),(0,4)],5)
 => [4,4,4,4,4,4]
 => [4,4,4,4,4]
 => ? = 2 - 2
([(0,2),(0,3),(0,4),(4,1)],5)
 => [4,4,4]
 => [4,4]
 => 0 = 2 - 2
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => [8]
 => []
 => ? = 2 - 2
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => [3,3]
 => [3]
 => 0 = 2 - 2
([(1,3),(1,4),(4,2)],5)
 => [15]
 => []
 => ? = 2 - 2
([(0,3),(0,4),(4,1),(4,2)],5)
 => [8]
 => []
 => ? = 2 - 2
([(1,2),(1,3),(2,4),(3,4)],5)
 => [5,5]
 => [5]
 => 0 = 2 - 2
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => [2]
 => []
 => ? = 2 - 2
([(0,3),(0,4),(3,2),(4,1)],5)
 => [4,2]
 => [2]
 => 0 = 2 - 2
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => [3,2]
 => [2]
 => 0 = 2 - 2
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => [2,2]
 => [2]
 => 0 = 2 - 2
([(2,3),(3,4)],5)
 => [5,5,5,5]
 => [5,5,5]
 => 0 = 2 - 2
([(1,4),(4,2),(4,3)],5)
 => [5,5]
 => [5]
 => 0 = 2 - 2
([(0,4),(4,1),(4,2),(4,3)],5)
 => [3,3]
 => [3]
 => 0 = 2 - 2
([(2,4),(3,4)],5)
 => [10,10,10,10]
 => [10,10,10]
 => ? = 2 - 2
([(1,4),(2,4),(4,3)],5)
 => [5,5]
 => [5]
 => 0 = 2 - 2
([(0,4),(1,4),(4,2),(4,3)],5)
 => [2,2]
 => [2]
 => 0 = 2 - 2
([(1,4),(2,4),(3,4)],5)
 => [15,15]
 => [15]
 => 0 = 2 - 2
([(0,4),(1,4),(2,4),(4,3)],5)
 => [3,3]
 => [3]
 => 0 = 2 - 2
([(0,4),(1,4),(2,4),(3,4)],5)
 => [4,4,4,4,4,4]
 => [4,4,4,4,4]
 => ? = 2 - 2
([(0,4),(1,4),(2,3)],5)
 => [10,10]
 => [10]
 => 0 = 2 - 2
([(0,4),(1,3),(2,3),(2,4)],5)
 => [12,4]
 => [4]
 => 0 = 2 - 2
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [14]
 => []
 => ? = 2 - 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [6,6]
 => [6]
 => 0 = 2 - 2
([(0,4),(1,4),(2,3),(4,2)],5)
 => [2]
 => []
 => ? = 2 - 2
([(0,4),(1,3),(2,3),(3,4)],5)
 => [8]
 => []
 => ? = 2 - 2
([(0,4),(1,4),(2,3),(2,4)],5)
 => [10,4,4]
 => [4,4]
 => 0 = 2 - 2
([(0,4),(1,4),(2,3),(3,4)],5)
 => [4,4,4]
 => [4,4]
 => 0 = 2 - 2
([(1,4),(2,3)],5)
 => [5,5,5,5,5,5]
 => [5,5,5,5,5]
 => ? = 2 - 2
([(1,4),(2,3),(2,4)],5)
 => [15,5,5]
 => [5,5]
 => 0 = 2 - 2
([(0,4),(1,2),(1,4),(2,3)],5)
 => [5,4]
 => [4]
 => 0 = 2 - 2
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
 => [3,2]
 => [2]
 => 0 = 2 - 2
([(1,3),(1,4),(2,3),(2,4)],5)
 => [5,5,5,5]
 => [5,5,5]
 => 0 = 2 - 2
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
 => [6]
 => []
 => ? = 2 - 2
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
 => [2,2]
 => [2]
 => 0 = 2 - 2
([(0,4),(1,2),(1,4),(4,3)],5)
 => [7]
 => []
 => ? = 2 - 2
([(0,4),(1,2),(1,3)],5)
 => [10,10]
 => [10]
 => 0 = 2 - 2
([(0,4),(1,2),(1,3),(1,4)],5)
 => [10,4,4]
 => [4,4]
 => 0 = 2 - 2
([(0,2),(0,4),(3,1),(4,3)],5)
 => [4]
 => []
 => ? = 2 - 2
([(0,4),(1,2),(1,3),(3,4)],5)
 => [4,4,3]
 => [4,3]
 => 0 = 2 - 2
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => [3]
 => []
 => ? = 2 - 2
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [8]
 => []
 => ? = 2 - 2
([(0,3),(0,4),(1,2),(1,4)],5)
 => [12,4]
 => [4]
 => 0 = 2 - 2
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => [14]
 => []
 => ? = 2 - 2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => [6,6]
 => [6]
 => 0 = 2 - 2
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
 => [5,3]
 => [3]
 => 0 = 2 - 2
([(0,3),(1,2),(1,4),(3,4)],5)
 => [5,4]
 => [4]
 => 0 = 2 - 2
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
 => [6]
 => []
 => ? = 2 - 2
([(1,4),(3,2),(4,3)],5)
 => [5]
 => []
 => ? = 2 - 2
([(0,3),(3,4),(4,1),(4,2)],5)
 => [2]
 => []
 => ? = 2 - 2
([(1,4),(2,3),(3,4)],5)
 => [15]
 => []
 => ? = 2 - 2
([(0,4),(1,2),(2,4),(4,3)],5)
 => [3]
 => []
 => ? = 2 - 2
([(0,3),(1,4),(4,2)],5)
 => [5,5]
 => [5]
 => 0 = 2 - 2
([(0,4),(3,2),(4,1),(4,3)],5)
 => [3]
 => []
 => ? = 2 - 2
([(0,4),(1,2),(2,3),(2,4)],5)
 => [7]
 => []
 => ? = 2 - 2
([(0,4),(2,3),(3,1),(4,2)],5)
 => [1]
 => []
 => ? = 1 - 2
([(0,3),(1,2),(2,4),(3,4)],5)
 => [4,2]
 => [2]
 => 0 = 2 - 2
([(0,4),(1,2),(2,3),(3,4)],5)
 => [4]
 => []
 => ? = 2 - 2
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => [2]
 => []
 => ? = 2 - 2
([],6)
 => [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]
 => ?
 => ? = 2 - 2
([(4,5)],6)
 => [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]
 => ?
 => ? = 2 - 2
([(3,4),(3,5)],6)
 => [12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12]
 => ?
 => ? = 2 - 2
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
 => [15,15]
 => [15]
 => 0 = 2 - 2
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => [3,3]
 => [3]
 => 0 = 2 - 2
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
 => [10,10]
 => [10]
 => 0 = 2 - 2
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6)
 => [12,4]
 => [4]
 => 0 = 2 - 2
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [6,6]
 => [6]
 => 0 = 2 - 2
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6)
 => [10,4,4]
 => [4,4]
 => 0 = 2 - 2
([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6)
 => [5,5]
 => [5]
 => 0 = 2 - 2
([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6)
 => [15,5,5]
 => [5,5]
 => 0 = 2 - 2
([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6)
 => [5,5,5,5]
 => [5,5,5]
 => 0 = 2 - 2
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
 => [15,15]
 => [15]
 => 0 = 2 - 2
Description
The number of ways to obtain a partition as the multiset of antidiagonal lengths of the Ferrers diagram of a partition. Given a partition λ⊢n, let α(λ) be the partition given by the lengths of the antidiagonals of the Ferrers diagram of λ. Then, the value of the statistic on μ is the number of times μ appears in the multiset {{α(λ)∣λ⊢n}}.
Matching statistic: St001593
Mapping
Mp00307: Posets —promotion cycle type⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
St001593: Integer partitions ⟶ ℤResult quality: 17% ●values known / values provided: 17%●distinct values known / distinct values provided: 33%
Values
([],1)
 => [1]
 => []
 => []
 => ? = 1 - 2
([],2)
 => [2]
 => []
 => []
 => ? = 2 - 2
([(0,1)],2)
 => [1]
 => []
 => []
 => ? = 1 - 2
([],3)
 => [3,3]
 => [3]
 => [1,1,1]
 => 0 = 2 - 2
([(1,2)],3)
 => [3]
 => []
 => []
 => ? = 2 - 2
([(0,1),(0,2)],3)
 => [2]
 => []
 => []
 => ? = 2 - 2
([(0,2),(2,1)],3)
 => [1]
 => []
 => []
 => ? = 1 - 2
([(0,2),(1,2)],3)
 => [2]
 => []
 => []
 => ? = 2 - 2
([],4)
 => [4,4,4,4,4,4]
 => [4,4,4,4,4]
 => [5,5,5,5]
 => ? = 2 - 2
([(2,3)],4)
 => [4,4,4]
 => [4,4]
 => [2,2,2,2]
 => 0 = 2 - 2
([(1,2),(1,3)],4)
 => [8]
 => []
 => []
 => ? = 2 - 2
([(0,1),(0,2),(0,3)],4)
 => [3,3]
 => [3]
 => [1,1,1]
 => 0 = 2 - 2
([(0,2),(0,3),(3,1)],4)
 => [3]
 => []
 => []
 => ? = 2 - 2
([(0,1),(0,2),(1,3),(2,3)],4)
 => [2]
 => []
 => []
 => ? = 2 - 2
([(1,2),(2,3)],4)
 => [4]
 => []
 => []
 => ? = 2 - 2
([(0,3),(3,1),(3,2)],4)
 => [2]
 => []
 => []
 => ? = 2 - 2
([(1,3),(2,3)],4)
 => [8]
 => []
 => []
 => ? = 2 - 2
([(0,3),(1,3),(3,2)],4)
 => [2]
 => []
 => []
 => ? = 2 - 2
([(0,3),(1,3),(2,3)],4)
 => [3,3]
 => [3]
 => [1,1,1]
 => 0 = 2 - 2
([(0,3),(1,2)],4)
 => [4,2]
 => [2]
 => [1,1]
 => 0 = 2 - 2
([(0,3),(1,2),(1,3)],4)
 => [3,2]
 => [2]
 => [1,1]
 => 0 = 2 - 2
([(0,2),(0,3),(1,2),(1,3)],4)
 => [2,2]
 => [2]
 => [1,1]
 => 0 = 2 - 2
([(0,3),(2,1),(3,2)],4)
 => [1]
 => []
 => []
 => ? = 1 - 2
([(0,3),(1,2),(2,3)],4)
 => [3]
 => []
 => []
 => ? = 2 - 2
([],5)
 => [5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5]
 => [5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5]
 => [23,23,23,23,23]
 => ? = 2 - 2
([(3,4)],5)
 => [5,5,5,5,5,5,5,5,5,5,5,5]
 => [5,5,5,5,5,5,5,5,5,5,5]
 => [11,11,11,11,11]
 => ? = 2 - 2
([(2,3),(2,4)],5)
 => [10,10,10,10]
 => [10,10,10]
 => [3,3,3,3,3,3,3,3,3,3]
 => ? = 2 - 2
([(1,2),(1,3),(1,4)],5)
 => [15,15]
 => [15]
 => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
 => 0 = 2 - 2
([(0,1),(0,2),(0,3),(0,4)],5)
 => [4,4,4,4,4,4]
 => [4,4,4,4,4]
 => [5,5,5,5]
 => ? = 2 - 2
([(0,2),(0,3),(0,4),(4,1)],5)
 => [4,4,4]
 => [4,4]
 => [2,2,2,2]
 => 0 = 2 - 2
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => [8]
 => []
 => []
 => ? = 2 - 2
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => [3,3]
 => [3]
 => [1,1,1]
 => 0 = 2 - 2
([(1,3),(1,4),(4,2)],5)
 => [15]
 => []
 => []
 => ? = 2 - 2
([(0,3),(0,4),(4,1),(4,2)],5)
 => [8]
 => []
 => []
 => ? = 2 - 2
([(1,2),(1,3),(2,4),(3,4)],5)
 => [5,5]
 => [5]
 => [1,1,1,1,1]
 => 0 = 2 - 2
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => [2]
 => []
 => []
 => ? = 2 - 2
([(0,3),(0,4),(3,2),(4,1)],5)
 => [4,2]
 => [2]
 => [1,1]
 => 0 = 2 - 2
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => [3,2]
 => [2]
 => [1,1]
 => 0 = 2 - 2
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => [2,2]
 => [2]
 => [1,1]
 => 0 = 2 - 2
([(2,3),(3,4)],5)
 => [5,5,5,5]
 => [5,5,5]
 => [3,3,3,3,3]
 => 0 = 2 - 2
([(1,4),(4,2),(4,3)],5)
 => [5,5]
 => [5]
 => [1,1,1,1,1]
 => 0 = 2 - 2
([(0,4),(4,1),(4,2),(4,3)],5)
 => [3,3]
 => [3]
 => [1,1,1]
 => 0 = 2 - 2
([(2,4),(3,4)],5)
 => [10,10,10,10]
 => [10,10,10]
 => [3,3,3,3,3,3,3,3,3,3]
 => ? = 2 - 2
([(1,4),(2,4),(4,3)],5)
 => [5,5]
 => [5]
 => [1,1,1,1,1]
 => 0 = 2 - 2
([(0,4),(1,4),(4,2),(4,3)],5)
 => [2,2]
 => [2]
 => [1,1]
 => 0 = 2 - 2
([(1,4),(2,4),(3,4)],5)
 => [15,15]
 => [15]
 => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
 => 0 = 2 - 2
([(0,4),(1,4),(2,4),(4,3)],5)
 => [3,3]
 => [3]
 => [1,1,1]
 => 0 = 2 - 2
([(0,4),(1,4),(2,4),(3,4)],5)
 => [4,4,4,4,4,4]
 => [4,4,4,4,4]
 => [5,5,5,5]
 => ? = 2 - 2
([(0,4),(1,4),(2,3)],5)
 => [10,10]
 => [10]
 => [1,1,1,1,1,1,1,1,1,1]
 => 0 = 2 - 2
([(0,4),(1,3),(2,3),(2,4)],5)
 => [12,4]
 => [4]
 => [1,1,1,1]
 => 0 = 2 - 2
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [14]
 => []
 => []
 => ? = 2 - 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [6,6]
 => [6]
 => [1,1,1,1,1,1]
 => 0 = 2 - 2
([(0,4),(1,4),(2,3),(4,2)],5)
 => [2]
 => []
 => []
 => ? = 2 - 2
([(0,4),(1,3),(2,3),(3,4)],5)
 => [8]
 => []
 => []
 => ? = 2 - 2
([(0,4),(1,4),(2,3),(2,4)],5)
 => [10,4,4]
 => [4,4]
 => [2,2,2,2]
 => 0 = 2 - 2
([(0,4),(1,4),(2,3),(3,4)],5)
 => [4,4,4]
 => [4,4]
 => [2,2,2,2]
 => 0 = 2 - 2
([(1,4),(2,3)],5)
 => [5,5,5,5,5,5]
 => [5,5,5,5,5]
 => [5,5,5,5,5]
 => ? = 2 - 2
([(1,4),(2,3),(2,4)],5)
 => [15,5,5]
 => [5,5]
 => [2,2,2,2,2]
 => 0 = 2 - 2
([(0,4),(1,2),(1,4),(2,3)],5)
 => [5,4]
 => [4]
 => [1,1,1,1]
 => 0 = 2 - 2
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
 => [3,2]
 => [2]
 => [1,1]
 => 0 = 2 - 2
([(1,3),(1,4),(2,3),(2,4)],5)
 => [5,5,5,5]
 => [5,5,5]
 => [3,3,3,3,3]
 => 0 = 2 - 2
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
 => [6]
 => []
 => []
 => ? = 2 - 2
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
 => [2,2]
 => [2]
 => [1,1]
 => 0 = 2 - 2
([(0,4),(1,2),(1,4),(4,3)],5)
 => [7]
 => []
 => []
 => ? = 2 - 2
([(0,4),(1,2),(1,3)],5)
 => [10,10]
 => [10]
 => [1,1,1,1,1,1,1,1,1,1]
 => 0 = 2 - 2
([(0,4),(1,2),(1,3),(1,4)],5)
 => [10,4,4]
 => [4,4]
 => [2,2,2,2]
 => 0 = 2 - 2
([(0,2),(0,4),(3,1),(4,3)],5)
 => [4]
 => []
 => []
 => ? = 2 - 2
([(0,4),(1,2),(1,3),(3,4)],5)
 => [4,4,3]
 => [4,3]
 => [2,2,2,1]
 => 0 = 2 - 2
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => [3]
 => []
 => []
 => ? = 2 - 2
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [8]
 => []
 => []
 => ? = 2 - 2
([(0,3),(0,4),(1,2),(1,4)],5)
 => [12,4]
 => [4]
 => [1,1,1,1]
 => 0 = 2 - 2
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => [14]
 => []
 => []
 => ? = 2 - 2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => [6,6]
 => [6]
 => [1,1,1,1,1,1]
 => 0 = 2 - 2
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
 => [5,3]
 => [3]
 => [1,1,1]
 => 0 = 2 - 2
([(0,3),(1,2),(1,4),(3,4)],5)
 => [5,4]
 => [4]
 => [1,1,1,1]
 => 0 = 2 - 2
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
 => [6]
 => []
 => []
 => ? = 2 - 2
([(1,4),(3,2),(4,3)],5)
 => [5]
 => []
 => []
 => ? = 2 - 2
([(0,3),(3,4),(4,1),(4,2)],5)
 => [2]
 => []
 => []
 => ? = 2 - 2
([(1,4),(2,3),(3,4)],5)
 => [15]
 => []
 => []
 => ? = 2 - 2
([(0,4),(1,2),(2,4),(4,3)],5)
 => [3]
 => []
 => []
 => ? = 2 - 2
([(0,3),(1,4),(4,2)],5)
 => [5,5]
 => [5]
 => [1,1,1,1,1]
 => 0 = 2 - 2
([(0,4),(3,2),(4,1),(4,3)],5)
 => [3]
 => []
 => []
 => ? = 2 - 2
([(0,4),(1,2),(2,3),(2,4)],5)
 => [7]
 => []
 => []
 => ? = 2 - 2
([(0,4),(2,3),(3,1),(4,2)],5)
 => [1]
 => []
 => []
 => ? = 1 - 2
([(0,3),(1,2),(2,4),(3,4)],5)
 => [4,2]
 => [2]
 => [1,1]
 => 0 = 2 - 2
([(0,4),(1,2),(2,3),(3,4)],5)
 => [4]
 => []
 => []
 => ? = 2 - 2
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => [2]
 => []
 => []
 => ? = 2 - 2
([],6)
 => [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]
 => ?
 => ?
 => ? = 2 - 2
([(4,5)],6)
 => [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]
 => ?
 => ?
 => ? = 2 - 2
([(3,4),(3,5)],6)
 => [12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12]
 => ?
 => ?
 => ? = 2 - 2
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
 => [15,15]
 => [15]
 => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
 => 0 = 2 - 2
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => [3,3]
 => [3]
 => [1,1,1]
 => 0 = 2 - 2
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
 => [10,10]
 => [10]
 => [1,1,1,1,1,1,1,1,1,1]
 => 0 = 2 - 2
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6)
 => [12,4]
 => [4]
 => [1,1,1,1]
 => 0 = 2 - 2
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [6,6]
 => [6]
 => [1,1,1,1,1,1]
 => 0 = 2 - 2
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6)
 => [10,4,4]
 => [4,4]
 => [2,2,2,2]
 => 0 = 2 - 2
([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6)
 => [5,5]
 => [5]
 => [1,1,1,1,1]
 => 0 = 2 - 2
([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6)
 => [15,5,5]
 => [5,5]
 => [2,2,2,2,2]
 => 0 = 2 - 2
([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6)
 => [5,5,5,5]
 => [5,5,5]
 => [3,3,3,3,3]
 => 0 = 2 - 2
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
 => [15,15]
 => [15]
 => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
 => 0 = 2 - 2
Description
This is the number of standard Young tableaux of the given shifted shape. For an integer partition λ=(λ1,…,λk), the shifted diagram is obtained by moving the i-th row in the diagram i−1 boxes to the right, i.e., λ∗={(i,j)|1≤i≤k,i≤j≤λi+i−1}. In particular, this statistic is zero if and only if λi+1=λi for some i.
Matching statistic: St000929
(load all 3 compositions to match this statistic)
Mapping
Mp00307: Posets —promotion cycle type⟶ Integer partitions
St000929: Integer partitions ⟶ ℤResult quality: 16% ●values known / values provided: 16%●distinct values known / distinct values provided: 33%
Values
([],1)
 => [1]
 => ? = 1 - 2
([],2)
 => [2]
 => 0 = 2 - 2
([(0,1)],2)
 => [1]
 => ? = 1 - 2
([],3)
 => [3,3]
 => 0 = 2 - 2
([(1,2)],3)
 => [3]
 => 0 = 2 - 2
([(0,1),(0,2)],3)
 => [2]
 => 0 = 2 - 2
([(0,2),(2,1)],3)
 => [1]
 => ? = 1 - 2
([(0,2),(1,2)],3)
 => [2]
 => 0 = 2 - 2
([],4)
 => [4,4,4,4,4,4]
 => ? = 2 - 2
([(2,3)],4)
 => [4,4,4]
 => 0 = 2 - 2
([(1,2),(1,3)],4)
 => [8]
 => 0 = 2 - 2
([(0,1),(0,2),(0,3)],4)
 => [3,3]
 => 0 = 2 - 2
([(0,2),(0,3),(3,1)],4)
 => [3]
 => 0 = 2 - 2
([(0,1),(0,2),(1,3),(2,3)],4)
 => [2]
 => 0 = 2 - 2
([(1,2),(2,3)],4)
 => [4]
 => 0 = 2 - 2
([(0,3),(3,1),(3,2)],4)
 => [2]
 => 0 = 2 - 2
([(1,3),(2,3)],4)
 => [8]
 => 0 = 2 - 2
([(0,3),(1,3),(3,2)],4)
 => [2]
 => 0 = 2 - 2
([(0,3),(1,3),(2,3)],4)
 => [3,3]
 => 0 = 2 - 2
([(0,3),(1,2)],4)
 => [4,2]
 => 0 = 2 - 2
([(0,3),(1,2),(1,3)],4)
 => [3,2]
 => 0 = 2 - 2
([(0,2),(0,3),(1,2),(1,3)],4)
 => [2,2]
 => 0 = 2 - 2
([(0,3),(2,1),(3,2)],4)
 => [1]
 => ? = 1 - 2
([(0,3),(1,2),(2,3)],4)
 => [3]
 => 0 = 2 - 2
([],5)
 => [5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5]
 => ? = 2 - 2
([(3,4)],5)
 => [5,5,5,5,5,5,5,5,5,5,5,5]
 => ? = 2 - 2
([(2,3),(2,4)],5)
 => [10,10,10,10]
 => ? = 2 - 2
([(1,2),(1,3),(1,4)],5)
 => [15,15]
 => ? = 2 - 2
([(0,1),(0,2),(0,3),(0,4)],5)
 => [4,4,4,4,4,4]
 => ? = 2 - 2
([(0,2),(0,3),(0,4),(4,1)],5)
 => [4,4,4]
 => 0 = 2 - 2
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => [8]
 => 0 = 2 - 2
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => [3,3]
 => 0 = 2 - 2
([(1,3),(1,4),(4,2)],5)
 => [15]
 => ? = 2 - 2
([(0,3),(0,4),(4,1),(4,2)],5)
 => [8]
 => 0 = 2 - 2
([(1,2),(1,3),(2,4),(3,4)],5)
 => [5,5]
 => 0 = 2 - 2
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => [2]
 => 0 = 2 - 2
([(0,3),(0,4),(3,2),(4,1)],5)
 => [4,2]
 => 0 = 2 - 2
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => [3,2]
 => 0 = 2 - 2
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => [2,2]
 => 0 = 2 - 2
([(2,3),(3,4)],5)
 => [5,5,5,5]
 => ? = 2 - 2
([(1,4),(4,2),(4,3)],5)
 => [5,5]
 => 0 = 2 - 2
([(0,4),(4,1),(4,2),(4,3)],5)
 => [3,3]
 => 0 = 2 - 2
([(2,4),(3,4)],5)
 => [10,10,10,10]
 => ? = 2 - 2
([(1,4),(2,4),(4,3)],5)
 => [5,5]
 => 0 = 2 - 2
([(0,4),(1,4),(4,2),(4,3)],5)
 => [2,2]
 => 0 = 2 - 2
([(1,4),(2,4),(3,4)],5)
 => [15,15]
 => ? = 2 - 2
([(0,4),(1,4),(2,4),(4,3)],5)
 => [3,3]
 => 0 = 2 - 2
([(0,4),(1,4),(2,4),(3,4)],5)
 => [4,4,4,4,4,4]
 => ? = 2 - 2
([(0,4),(1,4),(2,3)],5)
 => [10,10]
 => ? = 2 - 2
([(0,4),(1,3),(2,3),(2,4)],5)
 => [12,4]
 => ? = 2 - 2
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [14]
 => ? = 2 - 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [6,6]
 => 0 = 2 - 2
([(0,4),(1,4),(2,3),(4,2)],5)
 => [2]
 => 0 = 2 - 2
([(0,4),(1,3),(2,3),(3,4)],5)
 => [8]
 => 0 = 2 - 2
([(0,4),(1,4),(2,3),(2,4)],5)
 => [10,4,4]
 => ? = 2 - 2
([(0,4),(1,4),(2,3),(3,4)],5)
 => [4,4,4]
 => 0 = 2 - 2
([(1,4),(2,3)],5)
 => [5,5,5,5,5,5]
 => ? = 2 - 2
([(1,4),(2,3),(2,4)],5)
 => [15,5,5]
 => ? = 2 - 2
([(0,4),(1,2),(1,4),(2,3)],5)
 => [5,4]
 => 0 = 2 - 2
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
 => [3,2]
 => 0 = 2 - 2
([(1,3),(1,4),(2,3),(2,4)],5)
 => [5,5,5,5]
 => ? = 2 - 2
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
 => [6]
 => 0 = 2 - 2
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
 => [2,2]
 => 0 = 2 - 2
([(0,4),(1,2),(1,4),(4,3)],5)
 => [7]
 => 0 = 2 - 2
([(0,4),(1,2),(1,3)],5)
 => [10,10]
 => ? = 2 - 2
([(0,4),(1,2),(1,3),(1,4)],5)
 => [10,4,4]
 => ? = 2 - 2
([(0,2),(0,4),(3,1),(4,3)],5)
 => [4]
 => 0 = 2 - 2
([(0,4),(1,2),(1,3),(3,4)],5)
 => [4,4,3]
 => 0 = 2 - 2
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => [3]
 => 0 = 2 - 2
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [8]
 => 0 = 2 - 2
([(0,3),(0,4),(1,2),(1,4)],5)
 => [12,4]
 => ? = 2 - 2
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => [14]
 => ? = 2 - 2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => [6,6]
 => 0 = 2 - 2
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
 => [5,3]
 => 0 = 2 - 2
([(0,3),(1,2),(1,4),(3,4)],5)
 => [5,4]
 => 0 = 2 - 2
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
 => [6]
 => 0 = 2 - 2
([(1,4),(2,3),(3,4)],5)
 => [15]
 => ? = 2 - 2
([(0,4),(2,3),(3,1),(4,2)],5)
 => [1]
 => ? = 1 - 2
([],6)
 => [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]
 => ? = 2 - 2
([(4,5)],6)
 => [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]
 => ? = 2 - 2
([(3,4),(3,5)],6)
 => [12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12]
 => ? = 2 - 2
([(2,3),(2,4),(2,5)],6)
 => [18,18,18,18,18,18,18,18,18,18]
 => ? = 2 - 2
([(1,2),(1,3),(1,4),(1,5)],6)
 => [24,24,24,24,24,24]
 => ? = 2 - 2
([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
 => [5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5]
 => ? = 2 - 2
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
 => [5,5,5,5,5,5,5,5,5,5,5,5]
 => ? = 2 - 2
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
 => [10,10,10,10]
 => ? = 2 - 2
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
 => [15,15]
 => ? = 2 - 2
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => [4,4,4,4,4,4]
 => ? = 2 - 2
([(1,3),(1,4),(1,5),(5,2)],6)
 => [24,24,24]
 => ? = 2 - 2
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
 => [10,10,10,10]
 => ? = 2 - 2
([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
 => [48]
 => ? = 2 - 2
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
 => [18,18]
 => ? = 2 - 2
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
 => [10,10]
 => ? = 2 - 2
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6)
 => [12,4]
 => ? = 2 - 2
([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [14]
 => ? = 2 - 2
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6)
 => [10,4,4]
 => ? = 2 - 2
([(0,3),(0,4),(0,5),(4,2),(5,1)],6)
 => [5,5,5,5,5,5]
 => ? = 2 - 2
([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6)
 => [15,5,5]
 => ? = 2 - 2
([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6)
 => [5,5,5,5]
 => ? = 2 - 2
([(2,3),(2,4),(4,5)],6)
 => [18,18,18,18,18]
 => ? = 2 - 2
Description
The constant term of the character polynomial of an integer partition. The definition of the character polynomial can be found in [1]. Indeed, this constant term is 0 for partitions λ≠1n and 1 for λ=1n.
The following 60 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St000791The number of pairs of left tunnels, one strictly containing the other, of a Dyck path. St001139The number of occurrences of hills of size 2 in a Dyck path. St000980The number of boxes weakly below the path and above the diagonal that lie below at least two peaks. St000658The number of rises of length 2 of a Dyck path. St001568The smallest positive integer that does not appear twice in the partition. St001624The breadth of a lattice. St000659The number of rises of length at least 2 of a Dyck path. St000674The number of hills of a Dyck path. St001141The number of occurrences of hills of size 3 in a Dyck path. St001011Number of simple modules of projective dimension 2 in the Nakayama algebra corresponding to the Dyck path. St000264The girth of a graph, which is not a tree. St001204Call a CNakayama algebra (a Nakayama algebra with a cyclic quiver) with Kupisch series L=[c0,c1,...,cn−1] such that n=c0<ci for all i>0 a special CNakayama algebra. St001570The minimal number of edges to add to make a graph Hamiltonian. St001498The normalised height of a Nakayama algebra with magnitude 1. St001217The projective dimension of the indecomposable injective module I[n-2] in the corresponding Nakayama algebra with simples enumerated from 0 to n-1. St001257The dominant dimension of the double dual of A/J when A is the corresponding Nakayama algebra with Jacobson radical J. St001185The number of indecomposable injective modules of grade at least 2 in the corresponding Nakayama algebra. St001199The dominant dimension of eAe for the corresponding Nakayama algebra A with minimal faithful projective-injective module eA. 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. St000455The second largest eigenvalue of a graph if it is integral. St001720The minimal length of a chain of small intervals in a lattice. St001431Half of the Loewy length minus one of a modified stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001195The global dimension of the algebra A/AfA of the corresponding Nakayama algebra A with minimal left faithful projective-injective module Af. 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. St001630The global dimension of the incidence algebra of the lattice over the rational numbers. St001878The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L. St001060The distinguishing index of a graph. St000699The toughness times the least common multiple of 1,. St000456The monochromatic index of a connected graph. St001118The acyclic chromatic index of a graph. 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. St001629The coefficient of the integer composition in the quasisymmetric expansion of the relabelling action of the symmetric group on cycles. St001545The second Elser number of a connected graph. St000464The Schultz index of a connected graph. St001335The cardinality of a minimal cycle-isolating set of a graph. St000272The treewidth of a graph. St000536The pathwidth of a graph. St000544The cop number of a graph. St001029The size of the core of a graph. St001270The bandwidth of a graph. St001277The degeneracy of a graph. St001358The largest degree of a regular subgraph of a graph. St001494The Alon-Tarsi number of a graph. St001580The acyclic chromatic number of a graph. St001792The arboricity of a graph. St001883The mutual visibility number of a graph. St001951The number of factors in the disjoint direct product decomposition of the automorphism group of a graph. St001962The proper pathwidth of a graph. St000535The rank-width of a graph. St000537The cutwidth of a graph. St001331The size of the minimal feedback vertex set. St001592The maximal number of simple paths between any two different vertices of a graph. St001638The book thickness of a graph. St001644The dimension of a graph. St001743The discrepancy of a graph. St001746The coalition number of a graph. St001826The maximal number of leaves on a vertex of a graph.