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Identifier

St001717: Posets ⟶ ℤ

Values

([],1) => 1

([],2) => 1

([(0,1)],2) => 2

([],3) => 1

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

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

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

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

([],4) => 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

([],5) => 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

([(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) => 2

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

([],6) => 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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Description

The largest size of an interval in a poset.

Code

def statistic(P):
    return max(len(P.interval(x, y)) for x,y in P.relations_iterator())

Created

May 17, 2021 at 10:04 by Martin Rubey

Updated

May 17, 2021 at 10:04 by Martin Rubey