Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001815
Mapping
Mp00242: Dyck paths —Hessenberg poset⟶ Posets
St001815: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0]
 => ([],1)
 => 1
[1,0,1,0]
 => ([(0,1)],2)
 => 2
[1,1,0,0]
 => ([],2)
 => 3
[1,0,1,0,1,0]
 => ([(0,2),(2,1)],3)
 => 4
[1,0,1,1,0,0]
 => ([(0,2),(1,2)],3)
 => 6
[1,1,0,0,1,0]
 => ([(0,1),(0,2)],3)
 => 6
[1,1,0,1,0,0]
 => ([(1,2)],3)
 => 8
[1,1,1,0,0,0]
 => ([],3)
 => 13
[1,0,1,0,1,0,1,0]
 => ([(0,3),(2,1),(3,2)],4)
 => 8
[1,0,1,0,1,1,0,0]
 => ([(0,3),(1,3),(3,2)],4)
 => 12
[1,0,1,1,0,0,1,0]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 12
[1,0,1,1,0,1,0,0]
 => ([(0,3),(1,2),(2,3)],4)
 => 16
[1,0,1,1,1,0,0,0]
 => ([(0,3),(1,3),(2,3)],4)
 => 26
[1,1,0,0,1,0,1,0]
 => ([(0,3),(3,1),(3,2)],4)
 => 12
[1,1,0,0,1,1,0,0]
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 18
[1,1,0,1,0,0,1,0]
 => ([(0,2),(0,3),(3,1)],4)
 => 16
[1,1,0,1,0,1,0,0]
 => ([(0,3),(1,2),(1,3)],4)
 => 22
[1,1,0,1,1,0,0,0]
 => ([(1,3),(2,3)],4)
 => 32
[1,1,1,0,0,0,1,0]
 => ([(0,1),(0,2),(0,3)],4)
 => 26
[1,1,1,0,0,1,0,0]
 => ([(1,2),(1,3)],4)
 => 32
[1,1,1,0,1,0,0,0]
 => ([(2,3)],4)
 => 44
[1,1,1,1,0,0,0,0]
 => ([],4)
 => 75
[1,0,1,0,1,0,1,0,1,0]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 16
[1,0,1,0,1,0,1,1,0,0]
 => ([(0,4),(1,4),(2,3),(4,2)],5)
 => 24
[1,0,1,0,1,1,0,0,1,0]
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 24
[1,0,1,0,1,1,0,1,0,0]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => 32
[1,0,1,0,1,1,1,0,0,0]
 => ([(0,4),(1,4),(2,4),(4,3)],5)
 => 52
[1,0,1,1,0,0,1,0,1,0]
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 24
[1,0,1,1,0,0,1,1,0,0]
 => ([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
 => 36
[1,0,1,1,0,1,0,0,1,0]
 => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => 32
[1,0,1,1,0,1,0,1,0,0]
 => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
 => 44
[1,0,1,1,0,1,1,0,0,0]
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => 64
[1,0,1,1,1,0,0,0,1,0]
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 52
[1,0,1,1,1,0,0,1,0,0]
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 64
[1,0,1,1,1,0,1,0,0,0]
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 88
[1,0,1,1,1,1,0,0,0,0]
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 150
[1,1,0,0,1,0,1,0,1,0]
 => ([(0,3),(3,4),(4,1),(4,2)],5)
 => 24
[1,1,0,0,1,0,1,1,0,0]
 => ([(0,4),(1,4),(4,2),(4,3)],5)
 => 36
[1,1,0,0,1,1,0,0,1,0]
 => ([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => 36
[1,1,0,0,1,1,0,1,0,0]
 => ([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
 => 48
[1,1,0,0,1,1,1,0,0,0]
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 78
[1,1,0,1,0,0,1,0,1,0]
 => ([(0,4),(3,2),(4,1),(4,3)],5)
 => 32
[1,1,0,1,0,0,1,1,0,0]
 => ([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
 => 48
[1,1,0,1,0,1,0,0,1,0]
 => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => 44
[1,1,0,1,0,1,0,1,0,0]
 => ([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
 => 60
[1,1,0,1,0,1,1,0,0,0]
 => ([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 90
[1,1,0,1,1,0,0,0,1,0]
 => ([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => 64
[1,1,0,1,1,0,0,1,0,0]
 => ([(0,4),(1,2),(1,3),(3,4)],5)
 => 80
[1,1,0,1,1,0,1,0,0,0]
 => ([(0,4),(1,4),(2,3),(2,4)],5)
 => 114
[1,1,0,1,1,1,0,0,0,0]
 => ([(1,4),(2,4),(3,4)],5)
 => 176
Description
The number of order preserving surjections from a poset to a total order.