- FindStat

Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St000635
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St000635: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

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

$f(a) < f(b)$ .