- FindStat

edit this statistic or download as text // json

Identifier

St000909: Posets ⟶ ℤ

Values

([],1) => 1

([],2) => 2

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

([],3) => 3

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

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

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

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

([],4) => 4

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

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

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

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

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

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

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

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

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

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

([(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) => 1

([],5) => 5

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

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

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

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

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

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

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

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

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

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

([(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) => 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

([(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) => 1

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

([],6) => 6

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 1564 entries. <<<

search for individual values

searching the database for the individual values of this statistic

/ search for generating function

searching the database for statistics with the same generating function

click to show known generating functions

$F_{1} = q$

$F_{2} = q + q^{2}$

$F_{3} = 2\ q + 2\ q^{2} + q^{3}$

$F_{4} = 5\ q + 6\ q^{2} + 3\ q^{3} + 2\ q^{4}$

$F_{5} = 18\ q + 20\ q^{2} + 10\ q^{3} + 10\ q^{4} + 3\ q^{5} + 2\ q^{6}$

$F_{6} = 84\ q + 96\ q^{2} + 44\ q^{3} + 47\ q^{4} + 18\ q^{5} + 19\ q^{6} + 5\ q^{7} + 4\ q^{8} + q^{9}$

Description

The number of maximal chains of maximal size in a poset.

Code

def statistic(P):
    l = [len(a) for a in P.maximal_chains()]
    return l.count(max(l))

Created

Jul 21, 2017 at 15:13 by Martin Rubey

Updated

Mar 08, 2021 at 15:32 by Martin Rubey