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Identifier

St001106: Posets ⟶ ℤ

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) => 4

([(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) => 12

([(1,2),(1,3),(1,4)],5) => 12

([(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) => 4

([(0,3),(0,4),(4,1),(4,2)],5) => 4

([(1,2),(1,3),(2,4),(3,4)],5) => 4

([(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) => 4

([(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

([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 12

([(0,4),(1,4),(2,3),(4,2)],5) => 2

([(0,4),(1,3),(2,3),(3,4)],5) => 6

([(0,4),(1,4),(2,3),(2,4)],5) => 8

([(0,4),(1,4),(2,3),(3,4)],5) => 6

([(1,4),(2,3)],5) => 6

([(1,4),(2,3),(2,4)],5) => 9

([(0,4),(1,2),(1,4),(2,3)],5) => 3

([(0,3),(1,2),(1,3),(2,4),(3,4)],5) => 3

([(1,3),(1,4),(2,3),(2,4)],5) => 12

([(0,3),(0,4),(1,3),(1,4),(4,2)],5) => 4

([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5) => 4

([(0,4),(1,2),(1,4),(4,3)],5) => 3

([(0,4),(1,2),(1,3)],5) => 4

([(0,4),(1,2),(1,3),(1,4)],5) => 8

([(0,2),(0,4),(3,1),(4,3)],5) => 2

([(0,4),(1,2),(1,3),(3,4)],5) => 4

([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => 2

([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 4

([(0,3),(0,4),(1,2),(1,4)],5) => 4

([(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 8

([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 12

([(0,3),(0,4),(1,2),(1,3),(2,4)],5) => 4

([(0,3),(1,2),(1,4),(3,4)],5) => 3

([(0,3),(0,4),(1,2),(2,3),(2,4)],5) => 4

([(1,4),(3,2),(4,3)],5) => 2

([(0,3),(3,4),(4,1),(4,2)],5) => 2

([(1,4),(2,3),(3,4)],5) => 6

([(0,4),(1,2),(2,4),(4,3)],5) => 2

([(0,3),(1,4),(4,2)],5) => 2

([(0,4),(3,2),(4,1),(4,3)],5) => 2

([(0,4),(1,2),(2,3),(2,4)],5) => 3

([(0,4),(2,3),(3,1),(4,2)],5) => 1

([(0,3),(1,2),(2,4),(3,4)],5) => 2

([(0,4),(1,2),(2,3),(3,4)],5) => 2

([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 2

([],6) => 720

([(4,5)],6) => 120

([(3,4),(3,5)],6) => 48

([(2,3),(2,4),(2,5)],6) => 36

([(1,2),(1,3),(1,4),(1,5)],6) => 48

([(0,1),(0,2),(0,3),(0,4),(0,5)],6) => 120

([(0,2),(0,3),(0,4),(0,5),(5,1)],6) => 24

([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6) => 24

([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6) => 24

([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6) => 24

([(1,3),(1,4),(1,5),(5,2)],6) => 12

([(0,3),(0,4),(0,5),(5,1),(5,2)],6) => 12

([(1,2),(1,3),(1,4),(3,5),(4,5)],6) => 12

([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => 12

([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6) => 6

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Description

The number of supergreedy linear extensions of a poset.
A linear extension of a poset P with elements $\{x_1,\dots,x_n\}$ is supergreedy, 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, let $M$ be the set of minimal elements of $P\setminus X$. If there is an element of $M$ which covers an element $x_j$ in $X$, then let $x_{i+1}$ be one of these such that $j$ is maximal; otherwise, choose $x_{i+1}$ to be any element of $M$.

This statistic records the number of supergreedy linear extensions.

References

[1] Kierstead, H. A., Trotter, W. T. Super-greedy linear extensions of ordered sets MathSciNet:1018632

Code

def statistic(P):
    return sum(1 for i in P._hasse_diagram.supergreedy_linear_extensions_iterator())

Created

Feb 15, 2018 at 21:45 by Martin Rubey

Updated

Feb 16, 2018 at 10:02 by Martin Rubey