- FindStat

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Identifier

St001664: Posets ⟶ ℤ

Values

([],1) => 2

([],2) => 3

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

([],3) => 4

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

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

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

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

([],4) => 5

([(2,3)],4) => 7

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

([(0,1),(0,2),(0,3)],4) => 7

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

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

([(1,2),(2,3)],4) => 7

([(0,3),(3,1),(3,2)],4) => 7

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

([(0,3),(1,3),(3,2)],4) => 7

([(0,3),(1,3),(2,3)],4) => 7

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

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

([(0,2),(0,3),(1,2),(1,3)],4) => 7

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

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

([],5) => 6

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

([(2,3),(2,4)],5) => 11

([(1,2),(1,3),(1,4)],5) => 11

([(0,1),(0,2),(0,3),(0,4)],5) => 9

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

([(0,1),(0,2),(0,3),(2,4),(3,4)],5) => 14

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

([(1,3),(1,4),(4,2)],5) => 13

([(0,3),(0,4),(4,1),(4,2)],5) => 13

([(1,2),(1,3),(2,4),(3,4)],5) => 14

([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 11

([(0,3),(0,4),(3,2),(4,1)],5) => 10

([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 13

([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5) => 11

([(2,3),(3,4)],5) => 10

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

([(0,4),(4,1),(4,2),(4,3)],5) => 10

([(2,4),(3,4)],5) => 11

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

([(0,4),(1,4),(4,2),(4,3)],5) => 11

([(1,4),(2,4),(3,4)],5) => 11

([(0,4),(1,4),(2,4),(4,3)],5) => 10

([(0,4),(1,4),(2,4),(3,4)],5) => 9

([(0,4),(1,4),(2,3)],5) => 11

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

([(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 13

([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 10

([(0,4),(1,4),(2,3),(4,2)],5) => 9

([(0,4),(1,3),(2,3),(3,4)],5) => 13

([(0,4),(1,4),(2,3),(2,4)],5) => 13

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

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

([(1,4),(2,3),(2,4)],5) => 13

([(0,4),(1,2),(1,4),(2,3)],5) => 13

([(0,3),(1,2),(1,3),(2,4),(3,4)],5) => 13

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

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

([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5) => 11

([(0,4),(1,2),(1,4),(4,3)],5) => 13

([(0,4),(1,2),(1,3)],5) => 11

([(0,4),(1,2),(1,3),(1,4)],5) => 13

([(0,2),(0,4),(3,1),(4,3)],5) => 11

([(0,4),(1,2),(1,3),(3,4)],5) => 15

([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => 13

([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 14

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

([(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 13

([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 10

([(0,3),(0,4),(1,2),(1,3),(2,4)],5) => 13

([(0,3),(1,2),(1,4),(3,4)],5) => 13

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

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

([(0,3),(3,4),(4,1),(4,2)],5) => 9

([(1,4),(2,3),(3,4)],5) => 13

([(0,4),(1,2),(2,4),(4,3)],5) => 11

([(0,3),(1,4),(4,2)],5) => 9

([(0,4),(3,2),(4,1),(4,3)],5) => 11

([(0,4),(1,2),(2,3),(2,4)],5) => 13

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

([(0,3),(1,2),(2,4),(3,4)],5) => 10

([(0,4),(1,2),(2,3),(3,4)],5) => 11

([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 11

([],6) => 7

([(4,5)],6) => 11

([(3,4),(3,5)],6) => 14

([(2,3),(2,4),(2,5)],6) => 15

([(1,2),(1,3),(1,4),(1,5)],6) => 14

([(0,1),(0,2),(0,3),(0,4),(0,5)],6) => 11

([(0,2),(0,3),(0,4),(0,5),(5,1)],6) => 16

([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6) => 20

([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6) => 20

([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6) => 16

([(1,3),(1,4),(1,5),(5,2)],6) => 19

([(0,3),(0,4),(0,5),(5,1),(5,2)],6) => 19

([(1,2),(1,3),(1,4),(3,5),(4,5)],6) => 23

([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => 21

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$F_{1} = q^{2}$

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

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

$F_{4} = 2\ q^{5} + q^{6} + 7\ q^{7} + 6\ q^{8}$

$F_{5} = 2\ q^{6} + 8\ q^{9} + 7\ q^{10} + 15\ q^{11} + 10\ q^{12} + 17\ q^{13} + 3\ q^{14} + q^{15}$

$F_{6} = 2\ q^{7} + 2\ q^{10} + 6\ q^{11} + 2\ q^{12} + 9\ q^{13} + 15\ q^{14} + 14\ q^{15} + 17\ q^{16} + 29\ q^{17} + 35\ q^{18} + 25\ q^{19} + 32\ q^{20} + 50\ q^{21} + 20\ q^{22} + 35\ q^{23} + 10\ q^{24} + 13\ q^{25} + 2\ q^{26}$

Description

The number of non-isomorphic subposets of a poset.

Code

def statistic(P):
    return len(set(P.subposet(s).canonical_label() for s in subsets(P)))

Created

Jan 05, 2021 at 13:26 by Martin Rubey

Updated

Jan 05, 2021 at 13:26 by Martin Rubey