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Identifier

St001360: Integer partitions ⟶ ℤ

Values

[1] => 1

[2] => 2

[1,1] => 2

[3] => 3

[2,1] => 5

[1,1,1] => 3

[4] => 4

[3,1] => 8

[2,2] => 6

[2,1,1] => 8

[1,1,1,1] => 4

[5] => 5

[4,1] => 11

[3,2] => 11

[3,1,1] => 13

[2,2,1] => 11

[2,1,1,1] => 11

[1,1,1,1,1] => 5

[6] => 6

[5,1] => 14

[4,2] => 16

[4,1,1] => 18

[3,3] => 12

[3,2,1] => 21

[3,1,1,1] => 18

[2,2,2] => 12

[2,2,1,1] => 16

[2,1,1,1,1] => 14

[1,1,1,1,1,1] => 6

[7] => 7

[6,1] => 17

[5,2] => 21

[5,1,1] => 23

[4,3] => 19

[4,2,1] => 31

[4,1,1,1] => 25

[3,3,1] => 24

[3,2,2] => 24

[3,2,1,1] => 31

[3,1,1,1,1] => 23

[2,2,2,1] => 19

[2,2,1,1,1] => 21

[2,1,1,1,1,1] => 17

[1,1,1,1,1,1,1] => 7

[8] => 8

[7,1] => 20

[6,2] => 26

[6,1,1] => 28

[5,3] => 26

[5,2,1] => 41

[5,1,1,1] => 32

[4,4] => 20

[4,3,1] => 39

[4,2,2] => 36

[4,2,1,1] => 46

[4,1,1,1,1] => 32

[3,3,2] => 29

[3,3,1,1] => 36

[3,2,2,1] => 39

[3,2,1,1,1] => 41

[3,1,1,1,1,1] => 28

[2,2,2,2] => 20

[2,2,2,1,1] => 26

[2,2,1,1,1,1] => 26

[2,1,1,1,1,1,1] => 20

[1,1,1,1,1,1,1,1] => 8

[9] => 9

[8,1] => 23

[7,2] => 31

[7,1,1] => 33

[6,3] => 33

[6,2,1] => 51

[6,1,1,1] => 39

[5,4] => 29

[5,3,1] => 54

[5,2,2] => 48

[5,2,1,1] => 61

[5,1,1,1,1] => 41

[4,4,1] => 42

[4,3,2] => 49

[4,3,1,1] => 59

[4,2,2,1] => 59

[4,2,1,1,1] => 61

[4,1,1,1,1,1] => 39

[3,3,3] => 30

[3,3,2,1] => 49

[3,3,1,1,1] => 48

[3,2,2,2] => 42

[3,2,2,1,1] => 54

[3,2,1,1,1,1] => 51

[3,1,1,1,1,1,1] => 33

[2,2,2,2,1] => 29

[2,2,2,1,1,1] => 33

[2,2,1,1,1,1,1] => 31

[2,1,1,1,1,1,1,1] => 23

[1,1,1,1,1,1,1,1,1] => 9

[10] => 10

[9,1] => 26

[8,2] => 36

[8,1,1] => 38

[7,3] => 40

>>> Load all 1200 entries. <<<

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Description

The number of covering relations in Young's lattice below a partition.

References

[1] Hopkins, S. Formula for number of edges in Hasse diagram of Young's lattice interval MathOverflow:324546

Code

@cached_function
def YoungsLattice(n):
    return posets.YoungsLattice(n)

def statistic(la):
    Y = YoungsLattice(la.size())
    return len(Y.subposet(Y.principal_order_ideal(la)).cover_relations())

Created

Mar 03, 2019 at 21:56 by Martin Rubey

Updated

Mar 03, 2019 at 21:56 by Martin Rubey