Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001964
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Mapping
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00126: Permutations —cactus evacuation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001964: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1}}
 => [1] => [1] => ([],1)
 => 0
{{1,2}}
 => [2,1] => [2,1] => ([],2)
 => 0
{{1},{2}}
 => [1,2] => [1,2] => ([(0,1)],2)
 => 0
{{1,2,3}}
 => [2,3,1] => [2,1,3] => ([(0,2),(1,2)],3)
 => 0
{{1,3},{2}}
 => [3,2,1] => [3,2,1] => ([],3)
 => 0
{{1},{2},{3}}
 => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
 => 0
{{1,2,3,4}}
 => [2,3,4,1] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
 => 1
{{1,2,3},{4}}
 => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
 => 0
{{1,2,4},{3}}
 => [2,4,3,1] => [4,2,1,3] => ([(1,3),(2,3)],4)
 => 0
{{1,2},{3,4}}
 => [2,1,4,3] => [2,1,4,3] => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2
{{1,2},{3},{4}}
 => [2,1,3,4] => [2,3,4,1] => ([(1,2),(2,3)],4)
 => 0
{{1,3,4},{2}}
 => [3,2,4,1] => [3,2,4,1] => ([(1,3),(2,3)],4)
 => 0
{{1,4},{2,3}}
 => [4,3,2,1] => [4,3,2,1] => ([],4)
 => 0
{{1},{2,3,4}}
 => [1,3,4,2] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4)
 => 0
{{1},{2,3},{4}}
 => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 0
{{1},{2},{3,4}}
 => [1,2,4,3] => [4,1,2,3] => ([(1,2),(2,3)],4)
 => 0
{{1},{2},{3},{4}}
 => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 0
{{1,2,3,4,5}}
 => [2,3,4,5,1] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
 => 1
{{1,2,3,4},{5}}
 => [2,3,4,1,5] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
 => 1
{{1,2,3,5},{4}}
 => [2,3,5,4,1] => [5,2,1,3,4] => ([(1,4),(2,4),(4,3)],5)
 => 1
{{1,2,3},{4,5}}
 => [2,3,1,5,4] => [2,1,5,3,4] => ([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
 => 2
{{1,2,3},{4},{5}}
 => [2,3,1,4,5] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
 => 0
{{1,2,4,5},{3}}
 => [2,4,3,5,1] => [4,2,3,1,5] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 1
{{1,2,4},{3,5}}
 => [2,4,5,1,3] => [2,4,1,3,5] => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
 => 1
{{1,2,4},{3},{5}}
 => [2,4,3,1,5] => [2,4,3,1,5] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 1
{{1,2,5},{3,4}}
 => [2,5,4,3,1] => [5,4,2,1,3] => ([(2,4),(3,4)],5)
 => 0
{{1,2},{3,4,5}}
 => [2,1,4,5,3] => [2,1,4,5,3] => ([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
 => 2
{{1,2},{3,4},{5}}
 => [2,1,4,3,5] => [2,4,1,5,3] => ([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
 => 2
{{1,2,5},{3},{4}}
 => [2,5,3,4,1] => [5,2,3,1,4] => ([(1,4),(2,3),(3,4)],5)
 => 0
{{1,2},{3},{4,5}}
 => [2,1,3,5,4] => [2,1,3,5,4] => ([(0,4),(1,4),(4,2),(4,3)],5)
 => 2
{{1,2},{3},{4},{5}}
 => [2,1,3,4,5] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
 => 0
{{1,3,4,5},{2}}
 => [3,2,4,5,1] => [3,2,4,5,1] => ([(1,4),(2,4),(4,3)],5)
 => 1
{{1,3,4},{2},{5}}
 => [3,2,4,1,5] => [3,4,2,5,1] => ([(1,4),(2,3),(3,4)],5)
 => 0
{{1,3,5},{2,4}}
 => [3,4,5,2,1] => [3,2,1,4,5] => ([(0,4),(1,4),(2,4),(4,3)],5)
 => 2
{{1,3},{2,4,5}}
 => [3,4,1,5,2] => [3,1,4,2,5] => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
 => 1
{{1,3},{2,4},{5}}
 => [3,4,1,2,5] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
 => 0
{{1,3,5},{2},{4}}
 => [3,2,5,4,1] => [3,2,1,5,4] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 3
{{1,3},{2},{4},{5}}
 => [3,2,1,4,5] => [3,4,5,2,1] => ([(2,3),(3,4)],5)
 => 0
{{1,4,5},{2,3}}
 => [4,3,2,5,1] => [4,3,5,2,1] => ([(2,4),(3,4)],5)
 => 0
{{1,5},{2,3,4}}
 => [5,3,4,2,1] => [5,3,2,4,1] => ([(2,4),(3,4)],5)
 => 0
{{1},{2,3,4,5}}
 => [1,3,4,5,2] => [3,1,2,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
 => 1
{{1},{2,3,4},{5}}
 => [1,3,4,2,5] => [1,3,2,4,5] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
{{1},{2,3,5},{4}}
 => [1,3,5,4,2] => [5,3,1,2,4] => ([(1,4),(2,3),(3,4)],5)
 => 0
{{1},{2,3},{4,5}}
 => [1,3,2,5,4] => [3,1,5,2,4] => ([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
 => 2
{{1},{2,3},{4},{5}}
 => [1,3,2,4,5] => [1,3,4,2,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => 0
{{1,4,5},{2},{3}}
 => [4,2,3,5,1] => [4,2,3,5,1] => ([(1,4),(2,3),(3,4)],5)
 => 0
{{1,5},{2,4},{3}}
 => [5,4,3,2,1] => [5,4,3,2,1] => ([],5)
 => 0
{{1},{2,4,5},{3}}
 => [1,4,3,5,2] => [4,1,3,2,5] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 1
{{1},{2,4},{3,5}}
 => [1,4,5,2,3] => [4,5,1,2,3] => ([(0,3),(1,4),(4,2)],5)
 => 0
{{1},{2,4},{3},{5}}
 => [1,4,3,2,5] => [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],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.