Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001105
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Mapping
St001105: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],2)
 => 2
([(0,1)],2)
 => 1
([],3)
 => 6
([(1,2)],3)
 => 2
([(0,1),(0,2)],3)
 => 2
([(0,2),(2,1)],3)
 => 1
([(0,2),(1,2)],3)
 => 2
([],4)
 => 24
([(2,3)],4)
 => 6
([(1,2),(1,3)],4)
 => 6
([(0,1),(0,2),(0,3)],4)
 => 6
([(0,2),(0,3),(3,1)],4)
 => 2
([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(1,2),(2,3)],4)
 => 2
([(0,3),(3,1),(3,2)],4)
 => 2
([(1,3),(2,3)],4)
 => 6
([(0,3),(1,3),(3,2)],4)
 => 2
([(0,3),(1,3),(2,3)],4)
 => 6
([(0,3),(1,2)],4)
 => 2
([(0,3),(1,2),(1,3)],4)
 => 3
([(0,2),(0,3),(1,2),(1,3)],4)
 => 4
([(0,3),(2,1),(3,2)],4)
 => 1
([(0,3),(1,2),(2,3)],4)
 => 2
([],5)
 => 120
([(3,4)],5)
 => 24
([(2,3),(2,4)],5)
 => 24
([(1,2),(1,3),(1,4)],5)
 => 24
([(0,1),(0,2),(0,3),(0,4)],5)
 => 24
([(0,2),(0,3),(0,4),(4,1)],5)
 => 6
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => 6
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 6
([(1,3),(1,4),(4,2)],5)
 => 6
([(0,3),(0,4),(4,1),(4,2)],5)
 => 6
([(1,2),(1,3),(2,4),(3,4)],5)
 => 6
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 2
([(0,3),(0,4),(3,2),(4,1)],5)
 => 2
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => 3
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => 4
([(2,3),(3,4)],5)
 => 6
([(1,4),(4,2),(4,3)],5)
 => 6
([(0,4),(4,1),(4,2),(4,3)],5)
 => 6
([(2,4),(3,4)],5)
 => 24
([(1,4),(2,4),(4,3)],5)
 => 6
([(0,4),(1,4),(4,2),(4,3)],5)
 => 4
([(1,4),(2,4),(3,4)],5)
 => 24
([(0,4),(1,4),(2,4),(4,3)],5)
 => 6
([(0,4),(1,4),(2,4),(3,4)],5)
 => 24
([(0,4),(1,4),(2,3)],5)
 => 6
([(0,4),(1,3),(2,3),(2,4)],5)
 => 8
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 10
Description
The number of greedy linear extensions of a poset. A linear extension of a poset $P$ with elements $\{x_1,\dots,x_n\}$ is greedy, if it can be obtained by the following algorithm: * Step 1. Choose a minimal element $x_1$. * Step 2. Suppose $X=\{x_1,\dots,x_i\}$ have been chosen. If there is at least one minimal element of $P\setminus X$ which is greater than $x_i$ then choose $x_{i+1}$ to be any such minimal element; otherwise, choose $x_{i+1}$ to be any minimal element of $P\setminus X$. This statistic records the number of greedy linear extensions.