Your data matches 3 different statistics following compositions of up to 3 maps.
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Matching statistic: St001399
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Mapping
St001399: 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)
 => 3
([(1,2)],3)
 => 1
([(0,1),(0,2)],3)
 => 2
([(0,2),(2,1)],3)
 => 1
([(0,2),(1,2)],3)
 => 2
([],4)
 => 4
([(2,3)],4)
 => 2
([(1,2),(1,3)],4)
 => 2
([(0,1),(0,2),(0,3)],4)
 => 3
([(0,2),(0,3),(3,1)],4)
 => 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(1,2),(2,3)],4)
 => 1
([(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)
 => 3
([(0,3),(1,2)],4)
 => 2
([(0,3),(1,2),(1,3)],4)
 => 1
([(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)
 => 1
([],5)
 => 5
([(3,4)],5)
 => 3
([(2,3),(2,4)],5)
 => 2
([(1,2),(1,3),(1,4)],5)
 => 3
([(0,1),(0,2),(0,3),(0,4)],5)
 => 4
([(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)
 => 3
([(1,3),(1,4),(4,2)],5)
 => 1
([(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)
 => 1
([(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)
 => 3
([(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)
 => 3
([(0,4),(1,4),(2,4),(4,3)],5)
 => 3
([(0,4),(1,4),(2,4),(3,4)],5)
 => 4
([(0,4),(1,4),(2,3)],5)
 => 2
([(0,4),(1,3),(2,3),(2,4)],5)
 => 2
Description
The distinguishing number of a poset. This is the minimal number of colours needed to colour the vertices of a poset, such that only the trivial automorphism of the poset preserves the colouring. See also [[St000469]], which is the same concept for graphs.
Matching statistic: St000699
Mapping
Mp00074: Posets —to graph⟶ Graphs
Mp00117: Graphs —Ore closure⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
St000699: Graphs ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 14%
Values
([],1)
 => ([],1)
 => ([],1)
 => ([],1)
 => ? = 1 + 11
([],2)
 => ([],2)
 => ([],2)
 => ([],1)
 => ? = 2 + 11
([(0,1)],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1 + 11
([],3)
 => ([],3)
 => ([],3)
 => ([],1)
 => ? = 3 + 11
([(1,2)],3)
 => ([(1,2)],3)
 => ([(1,2)],3)
 => ([(0,1)],2)
 => ? = 1 + 11
([(0,1),(0,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ? = 2 + 11
([(0,2),(2,1)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ? = 1 + 11
([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ? = 2 + 11
([],4)
 => ([],4)
 => ([],4)
 => ([],1)
 => ? = 4 + 11
([(2,3)],4)
 => ([(2,3)],4)
 => ([(2,3)],4)
 => ([(0,1)],2)
 => ? = 2 + 11
([(1,2),(1,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ? = 2 + 11
([(0,1),(0,2),(0,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ? = 3 + 11
([(0,2),(0,3),(3,1)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,1)],2)
 => ? = 1 + 11
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],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)
 => ? = 2 + 11
([(1,2),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ? = 1 + 11
([(0,3),(3,1),(3,2)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ? = 2 + 11
([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ? = 2 + 11
([(0,3),(1,3),(3,2)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ? = 2 + 11
([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ? = 3 + 11
([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => ([(0,1)],2)
 => ? = 2 + 11
([(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,1)],2)
 => ? = 1 + 11
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],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)
 => ? = 2 + 11
([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,1)],2)
 => ? = 1 + 11
([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,1)],2)
 => ? = 1 + 11
([],5)
 => ([],5)
 => ([],5)
 => ([],1)
 => ? = 5 + 11
([(3,4)],5)
 => ([(3,4)],5)
 => ([(3,4)],5)
 => ([(0,1)],2)
 => ? = 3 + 11
([(2,3),(2,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ? = 2 + 11
([(1,2),(1,3),(1,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ? = 3 + 11
([(0,1),(0,2),(0,3),(0,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ? = 4 + 11
([(0,2),(0,3),(0,4),(4,1)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => ? = 2 + 11
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ? = 2 + 11
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ? = 3 + 11
([(1,3),(1,4),(4,2)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => ? = 1 + 11
([(0,3),(0,4),(4,1),(4,2)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => ? = 2 + 11
([(1,2),(1,3),(2,4),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ? = 2 + 11
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ? = 2 + 11
([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ? = 2 + 11
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ? = 1 + 11
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ? = 2 + 11
([(2,3),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ? = 2 + 11
([(1,4),(4,2),(4,3)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ? = 2 + 11
([(0,4),(4,1),(4,2),(4,3)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ? = 3 + 11
([(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ? = 2 + 11
([(1,4),(2,4),(4,3)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ? = 2 + 11
([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ? = 2 + 11
([(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ? = 3 + 11
([(0,4),(1,4),(2,4),(4,3)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ? = 3 + 11
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ? = 4 + 11
([(0,4),(1,4),(2,3)],5)
 => ([(0,1),(2,4),(3,4)],5)
 => ([(0,1),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ? = 2 + 11
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ? = 2 + 11
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 12 = 1 + 11
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 12 = 1 + 11
([(0,5),(1,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 12 = 1 + 11
([(0,2),(0,3),(0,4),(1,5),(3,5),(4,1)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 12 = 1 + 11
([(0,3),(0,4),(2,5),(3,2),(4,1),(4,5)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 12 = 1 + 11
([(1,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 12 = 1 + 11
([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 12 = 1 + 11
([(0,4),(1,2),(1,3),(2,5),(3,4),(4,5)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 12 = 1 + 11
([(0,3),(0,4),(2,5),(3,5),(4,1),(4,2)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 12 = 1 + 11
([(1,4),(1,5),(2,3),(2,4),(3,5)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 12 = 1 + 11
([(0,4),(0,5),(1,2),(1,4),(2,5),(4,3)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 12 = 1 + 11
([(0,4),(0,5),(1,2),(1,4),(2,5),(5,3)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 12 = 1 + 11
([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 12 = 1 + 11
([(0,4),(0,5),(1,2),(1,3),(1,4),(3,5)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 12 = 1 + 11
([(0,3),(0,4),(1,2),(1,4),(1,5),(3,5)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 12 = 1 + 11
([(0,2),(0,4),(2,5),(3,1),(3,5),(4,3)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 12 = 1 + 11
([(0,3),(1,2),(1,4),(2,5),(3,4),(3,5)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 12 = 1 + 11
([(0,4),(0,5),(1,2),(2,3),(2,5),(3,4)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 12 = 1 + 11
([(0,4),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 12 = 1 + 11
([(0,4),(1,2),(1,4),(2,5),(3,5),(4,3)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 12 = 1 + 11
([(0,4),(1,3),(1,5),(2,3),(2,4),(4,5)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 12 = 1 + 11
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 12 = 1 + 11
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 12 = 1 + 11
([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 12 = 1 + 11
Description
The toughness times the least common multiple of 1,...,n-1 of a non-complete graph. A graph $G$ is $t$-tough if $G$ cannot be split into $k$ different connected components by the removal of fewer than $tk$ vertices for all integers $k>1$. The toughness of $G$ is the maximal number $t$ such that $G$ is $t$-tough. It is a rational number except for the complete graph, where it is infinity. The toughness of a disconnected graph is zero. This statistic is the toughness multiplied by the least common multiple of $1,\dots,n-1$, where $n$ is the number of vertices of $G$.
Matching statistic: St001597
(load all 3 compositions to match this statistic)
Mapping
Mp00306: Posets —rowmotion cycle type⟶ Integer partitions
Mp00179: Integer partitions —to skew partition⟶ Skew partitions
St001597: Skew partitions ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 29%
Values
([],1)
 => [2]
 => [[2],[]]
 => 1
([],2)
 => [2,2]
 => [[2,2],[]]
 => 2
([(0,1)],2)
 => [3]
 => [[3],[]]
 => 1
([],3)
 => [2,2,2,2]
 => [[2,2,2,2],[]]
 => ? = 3
([(1,2)],3)
 => [6]
 => [[6],[]]
 => 1
([(0,1),(0,2)],3)
 => [3,2]
 => [[3,2],[]]
 => 2
([(0,2),(2,1)],3)
 => [4]
 => [[4],[]]
 => 1
([(0,2),(1,2)],3)
 => [3,2]
 => [[3,2],[]]
 => 2
([],4)
 => [2,2,2,2,2,2,2,2]
 => [[2,2,2,2,2,2,2,2],[]]
 => ? = 4
([(2,3)],4)
 => [6,6]
 => [[6,6],[]]
 => ? = 2
([(1,2),(1,3)],4)
 => [6,2,2]
 => [[6,2,2],[]]
 => ? = 2
([(0,1),(0,2),(0,3)],4)
 => [3,2,2,2]
 => [[3,2,2,2],[]]
 => ? = 3
([(0,2),(0,3),(3,1)],4)
 => [7]
 => [[7],[]]
 => 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => [4,2]
 => [[4,2],[]]
 => 2
([(1,2),(2,3)],4)
 => [4,4]
 => [[4,4],[]]
 => ? = 1
([(0,3),(3,1),(3,2)],4)
 => [4,2]
 => [[4,2],[]]
 => 2
([(1,3),(2,3)],4)
 => [6,2,2]
 => [[6,2,2],[]]
 => ? = 2
([(0,3),(1,3),(3,2)],4)
 => [4,2]
 => [[4,2],[]]
 => 2
([(0,3),(1,3),(2,3)],4)
 => [3,2,2,2]
 => [[3,2,2,2],[]]
 => ? = 3
([(0,3),(1,2)],4)
 => [3,3,3]
 => [[3,3,3],[]]
 => ? = 2
([(0,3),(1,2),(1,3)],4)
 => [5,3]
 => [[5,3],[]]
 => ? = 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => [3,2,2]
 => [[3,2,2],[]]
 => 2
([(0,3),(2,1),(3,2)],4)
 => [5]
 => [[5],[]]
 => 1
([(0,3),(1,2),(2,3)],4)
 => [7]
 => [[7],[]]
 => 1
([],5)
 => [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]
 => [[2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2],[]]
 => ? = 5
([(3,4)],5)
 => [6,6,6,6]
 => [[6,6,6,6],[]]
 => ? = 3
([(2,3),(2,4)],5)
 => [6,6,2,2,2,2]
 => [[6,6,2,2,2,2],[]]
 => ? = 2
([(1,2),(1,3),(1,4)],5)
 => [6,2,2,2,2,2,2]
 => [[6,2,2,2,2,2,2],[]]
 => ? = 3
([(0,1),(0,2),(0,3),(0,4)],5)
 => [3,2,2,2,2,2,2,2]
 => [[3,2,2,2,2,2,2,2],[]]
 => ? = 4
([(0,2),(0,3),(0,4),(4,1)],5)
 => [7,6]
 => [[7,6],[]]
 => ? = 2
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => [7,2,2]
 => [[7,2,2],[]]
 => ? = 2
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => [4,2,2,2]
 => [[4,2,2,2],[]]
 => ? = 3
([(1,3),(1,4),(4,2)],5)
 => [14]
 => [[14],[]]
 => ? = 1
([(0,3),(0,4),(4,1),(4,2)],5)
 => [7,2,2]
 => [[7,2,2],[]]
 => ? = 2
([(1,2),(1,3),(2,4),(3,4)],5)
 => [4,4,2,2]
 => [[4,4,2,2],[]]
 => ? = 2
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => [5,2]
 => [[5,2],[]]
 => 2
([(0,3),(0,4),(3,2),(4,1)],5)
 => [4,3,3]
 => [[4,3,3],[]]
 => ? = 2
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => [5,4]
 => [[5,4],[]]
 => ? = 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => [4,2,2]
 => [[4,2,2],[]]
 => ? = 2
([(2,3),(3,4)],5)
 => [4,4,4,4]
 => [[4,4,4,4],[]]
 => ? = 2
([(1,4),(4,2),(4,3)],5)
 => [4,4,2,2]
 => [[4,4,2,2],[]]
 => ? = 2
([(0,4),(4,1),(4,2),(4,3)],5)
 => [4,2,2,2]
 => [[4,2,2,2],[]]
 => ? = 3
([(2,4),(3,4)],5)
 => [6,6,2,2,2,2]
 => [[6,6,2,2,2,2],[]]
 => ? = 2
([(1,4),(2,4),(4,3)],5)
 => [4,4,2,2]
 => [[4,4,2,2],[]]
 => ? = 2
([(0,4),(1,4),(4,2),(4,3)],5)
 => [4,2,2]
 => [[4,2,2],[]]
 => ? = 2
([(1,4),(2,4),(3,4)],5)
 => [6,2,2,2,2,2,2]
 => [[6,2,2,2,2,2,2],[]]
 => ? = 3
([(0,4),(1,4),(2,4),(4,3)],5)
 => [4,2,2,2]
 => [[4,2,2,2],[]]
 => ? = 3
([(0,4),(1,4),(2,4),(3,4)],5)
 => [3,2,2,2,2,2,2,2]
 => [[3,2,2,2,2,2,2,2],[]]
 => ? = 4
([(0,4),(1,4),(2,3)],5)
 => [6,3,3,3]
 => [[6,3,3,3],[]]
 => ? = 2
([(0,4),(1,3),(2,3),(2,4)],5)
 => [8,3,2]
 => [[8,3,2],[]]
 => ? = 2
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [5,3,2,2]
 => [[5,3,2,2],[]]
 => ? = 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [3,2,2,2,2]
 => [[3,2,2,2,2],[]]
 => ? = 3
([(0,4),(1,4),(2,3),(4,2)],5)
 => [5,2]
 => [[5,2],[]]
 => 2
([(0,4),(1,3),(2,3),(3,4)],5)
 => [7,2,2]
 => [[7,2,2],[]]
 => ? = 2
([(0,4),(1,4),(2,3),(2,4)],5)
 => [6,5,3]
 => [[6,5,3],[]]
 => ? = 2
([(0,4),(1,4),(2,3),(3,4)],5)
 => [7,6]
 => [[7,6],[]]
 => ? = 2
([(1,4),(2,3)],5)
 => [6,6,6]
 => [[6,6,6],[]]
 => ? = 2
([(1,4),(2,3),(2,4)],5)
 => [10,6]
 => [[10,6],[]]
 => ? = 1
([(0,4),(1,2),(1,4),(2,3)],5)
 => [8,3]
 => [[8,3],[]]
 => ? = 1
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
 => [5,4]
 => [[5,4],[]]
 => ? = 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => [6,2,2,2,2]
 => [[6,2,2,2,2],[]]
 => ? = 2
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
 => [7,2]
 => [[7,2],[]]
 => ? = 2
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
 => [4,2,2]
 => [[4,2,2],[]]
 => ? = 2
([(0,4),(1,2),(1,4),(4,3)],5)
 => [10]
 => [[10],[]]
 => ? = 1
([(0,4),(1,2),(1,3)],5)
 => [6,3,3,3]
 => [[6,3,3,3],[]]
 => ? = 2
([(0,4),(1,2),(1,3),(1,4)],5)
 => [6,5,3]
 => [[6,5,3],[]]
 => ? = 2
([(0,3),(3,4),(4,1),(4,2)],5)
 => [5,2]
 => [[5,2],[]]
 => 2
([(0,4),(2,3),(3,1),(4,2)],5)
 => [6]
 => [[6],[]]
 => 1
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => [5,2]
 => [[5,2],[]]
 => 2
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => [7]
 => [[7],[]]
 => 1
Description
The Frobenius rank of a skew partition. This is the minimal number of border strips in a border strip decomposition of the skew partition.