Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St001964
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Mapping
St001964: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => 0
([],2)
 => 0
([(0,1)],2)
 => 0
([],3)
 => 0
([(0,1),(0,2)],3)
 => 0
([(0,2),(2,1)],3)
 => 0
([(0,2),(1,2)],3)
 => 0
([],4)
 => 0
([(0,1),(0,2),(0,3)],4)
 => 1
([(0,2),(0,3),(3,1)],4)
 => 0
([(0,1),(0,2),(1,3),(2,3)],4)
 => 0
([(1,2),(2,3)],4)
 => 0
([(0,3),(3,1),(3,2)],4)
 => 1
([(1,3),(2,3)],4)
 => 0
([(0,3),(1,3),(3,2)],4)
 => 1
([(0,3),(1,3),(2,3)],4)
 => 1
([(0,3),(1,2),(1,3)],4)
 => 0
([(0,2),(0,3),(1,2),(1,3)],4)
 => 2
([(0,3),(2,1),(3,2)],4)
 => 0
([(0,3),(1,2),(2,3)],4)
 => 0
([],5)
 => 0
([(0,1),(0,2),(0,3),(0,4)],5)
 => 2
([(0,2),(0,3),(0,4),(4,1)],5)
 => 1
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 1
([(0,3),(0,4),(4,1),(4,2)],5)
 => 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
([(0,3),(0,4),(3,2),(4,1)],5)
 => 0
([(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)
 => 0
([(0,4),(4,1),(4,2),(4,3)],5)
 => 2
([(2,4),(3,4)],5)
 => 0
([(1,4),(2,4),(4,3)],5)
 => 1
([(0,4),(1,4),(4,2),(4,3)],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)
 => 0
([(0,4),(1,3),(2,3),(2,4)],5)
 => 0
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 3
([(0,4),(1,4),(2,3),(4,2)],5)
 => 1
([(0,4),(1,3),(2,3),(3,4)],5)
 => 1
([(0,4),(1,4),(2,3),(2,4)],5)
 => 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => 1
([(0,4),(1,2),(1,4),(2,3)],5)
 => 0
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
 => 1
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
 => 2
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
 => 2
([(0,4),(1,2),(1,4),(4,3)],5)
 => 1
Description
The interval resolution global dimension of a poset. This is the cardinality of the longest chain of right minimal approximations by interval modules of an indecomposable module over the incidence algebra.
Matching statistic: St000741
Mapping
Mp00074: Posets —to graph⟶ Graphs
Mp00259: Graphs —vertex addition⟶ Graphs
St000741: Graphs ⟶ ℤResult quality: 25% ●values known / values provided: 26%●distinct values known / distinct values provided: 25%
Values
([],1)
 => ([],1)
 => ([],2)
 => 1 = 0 + 1
([],2)
 => ([],2)
 => ([],3)
 => 1 = 0 + 1
([(0,1)],2)
 => ([(0,1)],2)
 => ([(1,2)],3)
 => ? = 0 + 1
([],3)
 => ([],3)
 => ([],4)
 => 1 = 0 + 1
([(0,1),(0,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(1,3),(2,3)],4)
 => 1 = 0 + 1
([(0,2),(2,1)],3)
 => ([(0,2),(1,2)],3)
 => ([(1,3),(2,3)],4)
 => 1 = 0 + 1
([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(1,3),(2,3)],4)
 => 1 = 0 + 1
([],4)
 => ([],4)
 => ([],5)
 => 1 = 0 + 1
([(0,1),(0,2),(0,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(1,4),(2,4),(3,4)],5)
 => ? = 1 + 1
([(0,2),(0,3),(3,1)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(1,4),(2,3),(3,4)],5)
 => 1 = 0 + 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ? = 0 + 1
([(1,2),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(2,4),(3,4)],5)
 => 1 = 0 + 1
([(0,3),(3,1),(3,2)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(1,4),(2,4),(3,4)],5)
 => ? = 1 + 1
([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(2,4),(3,4)],5)
 => 1 = 0 + 1
([(0,3),(1,3),(3,2)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(1,4),(2,4),(3,4)],5)
 => ? = 1 + 1
([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(1,4),(2,4),(3,4)],5)
 => ? = 1 + 1
([(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(1,4),(2,3),(3,4)],5)
 => 1 = 0 + 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ? = 2 + 1
([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(1,4),(2,3),(3,4)],5)
 => 1 = 0 + 1
([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(1,4),(2,3),(3,4)],5)
 => 1 = 0 + 1
([],5)
 => ([],5)
 => ([],6)
 => 1 = 0 + 1
([(0,1),(0,2),(0,3),(0,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 2 + 1
([(0,2),(0,3),(0,4),(4,1)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(1,5),(2,5),(3,4),(4,5)],6)
 => ? = 1 + 1
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ? = 1 + 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)
 => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ? = 1 + 1
([(0,3),(0,4),(4,1),(4,2)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(1,5),(2,5),(3,4),(4,5)],6)
 => ? = 1 + 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ? = 1 + 1
([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 1 = 0 + 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ? = 1 + 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)
 => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ? = 2 + 1
([(2,3),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(3,5),(4,5)],6)
 => 1 = 0 + 1
([(0,4),(4,1),(4,2),(4,3)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 2 + 1
([(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(3,5),(4,5)],6)
 => 1 = 0 + 1
([(1,4),(2,4),(4,3)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(2,5),(3,5),(4,5)],6)
 => ? = 1 + 1
([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 2 + 1
([(0,4),(1,4),(2,4),(4,3)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 2 + 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 2 + 1
([(0,4),(1,4),(2,3)],5)
 => ([(0,1),(2,4),(3,4)],5)
 => ([(1,2),(3,5),(4,5)],6)
 => 1 = 0 + 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 1 = 0 + 1
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ? = 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)
 => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ? = 3 + 1
([(0,4),(1,4),(2,3),(4,2)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(1,5),(2,5),(3,4),(4,5)],6)
 => ? = 1 + 1
([(0,4),(1,3),(2,3),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(1,5),(2,5),(3,4),(4,5)],6)
 => ? = 1 + 1
([(0,4),(1,4),(2,3),(2,4)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(1,5),(2,5),(3,4),(4,5)],6)
 => ? = 1 + 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(1,5),(2,5),(3,4),(4,5)],6)
 => ? = 1 + 1
([(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 1 = 0 + 1
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ? = 1 + 1
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ? = 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)
 => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ? = 2 + 1
([(0,4),(1,2),(1,4),(4,3)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(1,5),(2,5),(3,4),(4,5)],6)
 => ? = 1 + 1
([(0,4),(1,2),(1,3),(1,4)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(1,5),(2,5),(3,4),(4,5)],6)
 => ? = 1 + 1
([(0,2),(0,4),(3,1),(4,3)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 1 = 0 + 1
([(0,4),(1,2),(1,3),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 1 = 0 + 1
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ? = 0 + 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ? = 1 + 1
([(0,3),(0,4),(1,2),(1,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 1 = 0 + 1
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ? = 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)
 => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ? = 3 + 1
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ? = 2 + 1
([(0,3),(1,2),(1,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 1 = 0 + 1
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ? = 2 + 1
([(1,4),(3,2),(4,3)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(2,5),(3,4),(4,5)],6)
 => 1 = 0 + 1
([(0,3),(3,4),(4,1),(4,2)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(1,5),(2,5),(3,4),(4,5)],6)
 => ? = 1 + 1
([(1,4),(2,3),(3,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(2,5),(3,4),(4,5)],6)
 => 1 = 0 + 1
([(0,4),(1,2),(2,4),(4,3)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(1,5),(2,5),(3,4),(4,5)],6)
 => ? = 1 + 1
([(0,3),(1,4),(4,2)],5)
 => ([(0,1),(2,4),(3,4)],5)
 => ([(1,2),(3,5),(4,5)],6)
 => 1 = 0 + 1
([(0,4),(3,2),(4,1),(4,3)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(1,5),(2,5),(3,4),(4,5)],6)
 => ? = 1 + 1
([(0,4),(1,2),(2,3),(2,4)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(1,5),(2,5),(3,4),(4,5)],6)
 => ? = 1 + 1
([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 1 = 0 + 1
([(0,3),(1,2),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 1 = 0 + 1
([(0,4),(1,2),(2,3),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 1 = 0 + 1
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ? = 1 + 1
([],6)
 => ([],6)
 => ([],7)
 => ? = 0 + 1
([(3,4),(4,5)],6)
 => ([(3,5),(4,5)],6)
 => ([(4,6),(5,6)],7)
 => ? = 0 + 1
([(2,3),(3,5),(5,4)],6)
 => ([(2,5),(3,4),(4,5)],6)
 => ([(3,6),(4,5),(5,6)],7)
 => ? = 0 + 1
([(3,5),(4,5)],6)
 => ([(3,5),(4,5)],6)
 => ([(4,6),(5,6)],7)
 => ? = 0 + 1
([(2,5),(3,5),(5,4)],6)
 => ([(2,5),(3,5),(4,5)],6)
 => ([(3,6),(4,6),(5,6)],7)
 => ? = 1 + 1
([(0,5),(1,5),(2,5),(3,5),(5,4)],6)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ? = 3 + 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ? = 3 + 1
([(0,5),(1,5),(2,5),(3,4),(5,3)],6)
 => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => ? = 2 + 1
Description
The Colin de Verdière graph invariant.