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Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St000635
Values
([],2)
=> 4
([(0,1)],2)
=> 1
([],3)
=> 27
([(1,2)],3)
=> 3
([(0,1),(0,2)],3)
=> 4
([(0,2),(2,1)],3)
=> 1
([(0,2),(1,2)],3)
=> 4
([],4)
=> 256
([(2,3)],4)
=> 16
([(1,2),(1,3)],4)
=> 16
([(0,1),(0,2),(0,3)],4)
=> 27
([(0,2),(0,3),(3,1)],4)
=> 2
([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
([(1,2),(2,3)],4)
=> 4
([(0,3),(3,1),(3,2)],4)
=> 4
([(1,3),(2,3)],4)
=> 16
([(0,3),(1,3),(3,2)],4)
=> 4
([(0,3),(1,3),(2,3)],4)
=> 27
([(0,3),(1,2)],4)
=> 4
([(0,3),(1,2),(1,3)],4)
=> 8
([(0,2),(0,3),(1,2),(1,3)],4)
=> 16
([(0,3),(2,1),(3,2)],4)
=> 1
([(0,3),(1,2),(2,3)],4)
=> 2
([],5)
=> 3125
([(3,4)],5)
=> 125
([(2,3),(2,4)],5)
=> 100
([(1,2),(1,3),(1,4)],5)
=> 135
([(0,1),(0,2),(0,3),(0,4)],5)
=> 256
([(0,2),(0,3),(0,4),(4,1)],5)
=> 9
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
=> 12
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 27
([(1,3),(1,4),(4,2)],5)
=> 10
([(0,3),(0,4),(4,1),(4,2)],5)
=> 8
([(1,2),(1,3),(2,4),(3,4)],5)
=> 20
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 4
([(0,3),(0,4),(3,2),(4,1)],5)
=> 4
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> 8
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> 16
([(2,3),(3,4)],5)
=> 25
([(1,4),(4,2),(4,3)],5)
=> 20
([(0,4),(4,1),(4,2),(4,3)],5)
=> 27
([(2,4),(3,4)],5)
=> 100
([(1,4),(2,4),(4,3)],5)
=> 20
([(0,4),(1,4),(4,2),(4,3)],5)
=> 16
([(1,4),(2,4),(3,4)],5)
=> 135
([(0,4),(1,4),(2,4),(4,3)],5)
=> 27
([(0,4),(1,4),(2,4),(3,4)],5)
=> 256
([(0,4),(1,4),(2,3)],5)
=> 15
([(0,4),(1,3),(2,3),(2,4)],5)
=> 24
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> 55
Description
The number of strictly order preserving maps of a poset into itself.
A map $f$ is strictly order preserving if $a < b$ implies $f(a) < f(b)$.
Matching statistic: St001605
Mp00198: Posets —incomparability graph⟶ Graphs
Mp00037: Graphs —to partition of connected components⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001605: Integer partitions ⟶ ℤResult quality: 10% ●values known / values provided: 10%●distinct values known / distinct values provided: 12%
Mp00037: Graphs —to partition of connected components⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001605: Integer partitions ⟶ ℤResult quality: 10% ●values known / values provided: 10%●distinct values known / distinct values provided: 12%
Values
([],2)
=> ([(0,1)],2)
=> [2]
=> []
=> ? ∊ {1,4}
([(0,1)],2)
=> ([],2)
=> [1,1]
=> [1]
=> ? ∊ {1,4}
([],3)
=> ([(0,1),(0,2),(1,2)],3)
=> [3]
=> []
=> ? ∊ {1,3,4,4,27}
([(1,2)],3)
=> ([(0,2),(1,2)],3)
=> [3]
=> []
=> ? ∊ {1,3,4,4,27}
([(0,1),(0,2)],3)
=> ([(1,2)],3)
=> [2,1]
=> [1]
=> ? ∊ {1,3,4,4,27}
([(0,2),(2,1)],3)
=> ([],3)
=> [1,1,1]
=> [1,1]
=> ? ∊ {1,3,4,4,27}
([(0,2),(1,2)],3)
=> ([(1,2)],3)
=> [2,1]
=> [1]
=> ? ∊ {1,3,4,4,27}
([],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> []
=> ? ∊ {1,2,4,4,4,4,4,8,16,16,16,16,27,27,256}
([(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> []
=> ? ∊ {1,2,4,4,4,4,4,8,16,16,16,16,27,27,256}
([(1,2),(1,3)],4)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> []
=> ? ∊ {1,2,4,4,4,4,4,8,16,16,16,16,27,27,256}
([(0,1),(0,2),(0,3)],4)
=> ([(1,2),(1,3),(2,3)],4)
=> [3,1]
=> [1]
=> ? ∊ {1,2,4,4,4,4,4,8,16,16,16,16,27,27,256}
([(0,2),(0,3),(3,1)],4)
=> ([(1,3),(2,3)],4)
=> [3,1]
=> [1]
=> ? ∊ {1,2,4,4,4,4,4,8,16,16,16,16,27,27,256}
([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(2,3)],4)
=> [2,1,1]
=> [1,1]
=> ? ∊ {1,2,4,4,4,4,4,8,16,16,16,16,27,27,256}
([(1,2),(2,3)],4)
=> ([(0,3),(1,3),(2,3)],4)
=> [4]
=> []
=> ? ∊ {1,2,4,4,4,4,4,8,16,16,16,16,27,27,256}
([(0,3),(3,1),(3,2)],4)
=> ([(2,3)],4)
=> [2,1,1]
=> [1,1]
=> ? ∊ {1,2,4,4,4,4,4,8,16,16,16,16,27,27,256}
([(1,3),(2,3)],4)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> []
=> ? ∊ {1,2,4,4,4,4,4,8,16,16,16,16,27,27,256}
([(0,3),(1,3),(3,2)],4)
=> ([(2,3)],4)
=> [2,1,1]
=> [1,1]
=> ? ∊ {1,2,4,4,4,4,4,8,16,16,16,16,27,27,256}
([(0,3),(1,3),(2,3)],4)
=> ([(1,2),(1,3),(2,3)],4)
=> [3,1]
=> [1]
=> ? ∊ {1,2,4,4,4,4,4,8,16,16,16,16,27,27,256}
([(0,3),(1,2)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> [4]
=> []
=> ? ∊ {1,2,4,4,4,4,4,8,16,16,16,16,27,27,256}
([(0,3),(1,2),(1,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> [4]
=> []
=> ? ∊ {1,2,4,4,4,4,4,8,16,16,16,16,27,27,256}
([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,3),(1,2)],4)
=> [2,2]
=> [2]
=> ? ∊ {1,2,4,4,4,4,4,8,16,16,16,16,27,27,256}
([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> [1,1,1,1]
=> [1,1,1]
=> 2
([(0,3),(1,2),(2,3)],4)
=> ([(1,3),(2,3)],4)
=> [3,1]
=> [1]
=> ? ∊ {1,2,4,4,4,4,4,8,16,16,16,16,27,27,256}
([],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ? ∊ {3,3,3,4,4,4,4,4,4,4,5,6,8,8,8,8,8,8,9,9,10,10,12,12,15,15,16,16,16,20,20,20,20,24,24,25,27,27,27,38,38,40,55,55,80,100,100,108,108,125,135,135,256,256,3125}
([(3,4)],5)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ? ∊ {3,3,3,4,4,4,4,4,4,4,5,6,8,8,8,8,8,8,9,9,10,10,12,12,15,15,16,16,16,20,20,20,20,24,24,25,27,27,27,38,38,40,55,55,80,100,100,108,108,125,135,135,256,256,3125}
([(2,3),(2,4)],5)
=> ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ? ∊ {3,3,3,4,4,4,4,4,4,4,5,6,8,8,8,8,8,8,9,9,10,10,12,12,15,15,16,16,16,20,20,20,20,24,24,25,27,27,27,38,38,40,55,55,80,100,100,108,108,125,135,135,256,256,3125}
([(1,2),(1,3),(1,4)],5)
=> ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ? ∊ {3,3,3,4,4,4,4,4,4,4,5,6,8,8,8,8,8,8,9,9,10,10,12,12,15,15,16,16,16,20,20,20,20,24,24,25,27,27,27,38,38,40,55,55,80,100,100,108,108,125,135,135,256,256,3125}
([(0,1),(0,2),(0,3),(0,4)],5)
=> ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> ? ∊ {3,3,3,4,4,4,4,4,4,4,5,6,8,8,8,8,8,8,9,9,10,10,12,12,15,15,16,16,16,20,20,20,20,24,24,25,27,27,27,38,38,40,55,55,80,100,100,108,108,125,135,135,256,256,3125}
([(0,2),(0,3),(0,4),(4,1)],5)
=> ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> ? ∊ {3,3,3,4,4,4,4,4,4,4,5,6,8,8,8,8,8,8,9,9,10,10,12,12,15,15,16,16,16,20,20,20,20,24,24,25,27,27,27,38,38,40,55,55,80,100,100,108,108,125,135,135,256,256,3125}
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
=> ([(1,4),(2,3),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> ? ∊ {3,3,3,4,4,4,4,4,4,4,5,6,8,8,8,8,8,8,9,9,10,10,12,12,15,15,16,16,16,20,20,20,20,24,24,25,27,27,27,38,38,40,55,55,80,100,100,108,108,125,135,135,256,256,3125}
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> ([(2,3),(2,4),(3,4)],5)
=> [3,1,1]
=> [1,1]
=> ? ∊ {3,3,3,4,4,4,4,4,4,4,5,6,8,8,8,8,8,8,9,9,10,10,12,12,15,15,16,16,16,20,20,20,20,24,24,25,27,27,27,38,38,40,55,55,80,100,100,108,108,125,135,135,256,256,3125}
([(1,3),(1,4),(4,2)],5)
=> ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ? ∊ {3,3,3,4,4,4,4,4,4,4,5,6,8,8,8,8,8,8,9,9,10,10,12,12,15,15,16,16,16,20,20,20,20,24,24,25,27,27,27,38,38,40,55,55,80,100,100,108,108,125,135,135,256,256,3125}
([(0,3),(0,4),(4,1),(4,2)],5)
=> ([(1,4),(2,3),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> ? ∊ {3,3,3,4,4,4,4,4,4,4,5,6,8,8,8,8,8,8,9,9,10,10,12,12,15,15,16,16,16,20,20,20,20,24,24,25,27,27,27,38,38,40,55,55,80,100,100,108,108,125,135,135,256,256,3125}
([(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ? ∊ {3,3,3,4,4,4,4,4,4,4,5,6,8,8,8,8,8,8,9,9,10,10,12,12,15,15,16,16,16,20,20,20,20,24,24,25,27,27,27,38,38,40,55,55,80,100,100,108,108,125,135,135,256,256,3125}
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([(3,4)],5)
=> [2,1,1,1]
=> [1,1,1]
=> 2
([(0,3),(0,4),(3,2),(4,1)],5)
=> ([(1,3),(1,4),(2,3),(2,4)],5)
=> [4,1]
=> [1]
=> ? ∊ {3,3,3,4,4,4,4,4,4,4,5,6,8,8,8,8,8,8,9,9,10,10,12,12,15,15,16,16,16,20,20,20,20,24,24,25,27,27,27,38,38,40,55,55,80,100,100,108,108,125,135,135,256,256,3125}
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> ([(1,4),(2,3),(3,4)],5)
=> [4,1]
=> [1]
=> ? ∊ {3,3,3,4,4,4,4,4,4,4,5,6,8,8,8,8,8,8,9,9,10,10,12,12,15,15,16,16,16,20,20,20,20,24,24,25,27,27,27,38,38,40,55,55,80,100,100,108,108,125,135,135,256,256,3125}
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(1,4),(2,3)],5)
=> [2,2,1]
=> [2,1]
=> 1
([(2,3),(3,4)],5)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ? ∊ {3,3,3,4,4,4,4,4,4,4,5,6,8,8,8,8,8,8,9,9,10,10,12,12,15,15,16,16,16,20,20,20,20,24,24,25,27,27,27,38,38,40,55,55,80,100,100,108,108,125,135,135,256,256,3125}
([(1,4),(4,2),(4,3)],5)
=> ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ? ∊ {3,3,3,4,4,4,4,4,4,4,5,6,8,8,8,8,8,8,9,9,10,10,12,12,15,15,16,16,16,20,20,20,20,24,24,25,27,27,27,38,38,40,55,55,80,100,100,108,108,125,135,135,256,256,3125}
([(0,4),(4,1),(4,2),(4,3)],5)
=> ([(2,3),(2,4),(3,4)],5)
=> [3,1,1]
=> [1,1]
=> ? ∊ {3,3,3,4,4,4,4,4,4,4,5,6,8,8,8,8,8,8,9,9,10,10,12,12,15,15,16,16,16,20,20,20,20,24,24,25,27,27,27,38,38,40,55,55,80,100,100,108,108,125,135,135,256,256,3125}
([(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ? ∊ {3,3,3,4,4,4,4,4,4,4,5,6,8,8,8,8,8,8,9,9,10,10,12,12,15,15,16,16,16,20,20,20,20,24,24,25,27,27,27,38,38,40,55,55,80,100,100,108,108,125,135,135,256,256,3125}
([(1,4),(2,4),(4,3)],5)
=> ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ? ∊ {3,3,3,4,4,4,4,4,4,4,5,6,8,8,8,8,8,8,9,9,10,10,12,12,15,15,16,16,16,20,20,20,20,24,24,25,27,27,27,38,38,40,55,55,80,100,100,108,108,125,135,135,256,256,3125}
([(0,4),(1,4),(4,2),(4,3)],5)
=> ([(1,4),(2,3)],5)
=> [2,2,1]
=> [2,1]
=> 1
([(1,4),(2,4),(3,4)],5)
=> ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ? ∊ {3,3,3,4,4,4,4,4,4,4,5,6,8,8,8,8,8,8,9,9,10,10,12,12,15,15,16,16,16,20,20,20,20,24,24,25,27,27,27,38,38,40,55,55,80,100,100,108,108,125,135,135,256,256,3125}
([(0,4),(1,4),(2,4),(4,3)],5)
=> ([(2,3),(2,4),(3,4)],5)
=> [3,1,1]
=> [1,1]
=> ? ∊ {3,3,3,4,4,4,4,4,4,4,5,6,8,8,8,8,8,8,9,9,10,10,12,12,15,15,16,16,16,20,20,20,20,24,24,25,27,27,27,38,38,40,55,55,80,100,100,108,108,125,135,135,256,256,3125}
([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> ? ∊ {3,3,3,4,4,4,4,4,4,4,5,6,8,8,8,8,8,8,9,9,10,10,12,12,15,15,16,16,16,20,20,20,20,24,24,25,27,27,27,38,38,40,55,55,80,100,100,108,108,125,135,135,256,256,3125}
([(0,4),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> [5]
=> []
=> ? ∊ {3,3,3,4,4,4,4,4,4,4,5,6,8,8,8,8,8,8,9,9,10,10,12,12,15,15,16,16,16,20,20,20,20,24,24,25,27,27,27,38,38,40,55,55,80,100,100,108,108,125,135,135,256,256,3125}
([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ? ∊ {3,3,3,4,4,4,4,4,4,4,5,6,8,8,8,8,8,8,9,9,10,10,12,12,15,15,16,16,16,20,20,20,20,24,24,25,27,27,27,38,38,40,55,55,80,100,100,108,108,125,135,135,256,256,3125}
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> [5]
=> []
=> ? ∊ {3,3,3,4,4,4,4,4,4,4,5,6,8,8,8,8,8,8,9,9,10,10,12,12,15,15,16,16,16,20,20,20,20,24,24,25,27,27,27,38,38,40,55,55,80,100,100,108,108,125,135,135,256,256,3125}
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1),(2,3),(2,4),(3,4)],5)
=> [3,2]
=> [2]
=> ? ∊ {3,3,3,4,4,4,4,4,4,4,5,6,8,8,8,8,8,8,9,9,10,10,12,12,15,15,16,16,16,20,20,20,20,24,24,25,27,27,27,38,38,40,55,55,80,100,100,108,108,125,135,135,256,256,3125}
([(0,4),(1,4),(2,3),(4,2)],5)
=> ([(3,4)],5)
=> [2,1,1,1]
=> [1,1,1]
=> 2
([(0,4),(1,3),(2,3),(3,4)],5)
=> ([(1,4),(2,3),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> ? ∊ {3,3,3,4,4,4,4,4,4,4,5,6,8,8,8,8,8,8,9,9,10,10,12,12,15,15,16,16,16,20,20,20,20,24,24,25,27,27,27,38,38,40,55,55,80,100,100,108,108,125,135,135,256,256,3125}
([(0,4),(1,4),(2,3),(2,4)],5)
=> ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ? ∊ {3,3,3,4,4,4,4,4,4,4,5,6,8,8,8,8,8,8,9,9,10,10,12,12,15,15,16,16,16,20,20,20,20,24,24,25,27,27,27,38,38,40,55,55,80,100,100,108,108,125,135,135,256,256,3125}
([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> ? ∊ {3,3,3,4,4,4,4,4,4,4,5,6,8,8,8,8,8,8,9,9,10,10,12,12,15,15,16,16,16,20,20,20,20,24,24,25,27,27,27,38,38,40,55,55,80,100,100,108,108,125,135,135,256,256,3125}
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> ([(1,4),(2,3)],5)
=> [2,2,1]
=> [2,1]
=> 1
([(0,3),(3,4),(4,1),(4,2)],5)
=> ([(3,4)],5)
=> [2,1,1,1]
=> [1,1,1]
=> 2
([(0,4),(2,3),(3,1),(4,2)],5)
=> ([],5)
=> [1,1,1,1,1]
=> [1,1,1,1]
=> 6
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> ([(3,4)],5)
=> [2,1,1,1]
=> [1,1,1]
=> 2
Description
The number of colourings of a cycle such that the multiplicities of colours are given by a partition.
Two colourings are considered equal, if they are obtained by an action of the cyclic group.
This statistic is only defined for partitions of size at least 3, to avoid ambiguity.
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