- FindStat

Identifier

St001562: Integer partitions ⟶ ℤ

Values

[1] => 1
[2] => 1
[1,1] => 4
[3] => 1
[2,1] => 6
[1,1,1] => 27
[4] => 1
[3,1] => 8
[2,2] => 9
[2,1,1] => 54
[1,1,1,1] => 256
[5] => 1
[4,1] => 10
[3,2] => 12
[3,1,1] => 90
[2,2,1] => 108
[2,1,1,1] => 640
[1,1,1,1,1] => 3125
[6] => 1
[5,1] => 12
[4,2] => 15
[4,1,1] => 135
[3,3] => 16
[3,2,1] => 180
[3,1,1,1] => 1280
[2,2,2] => 216
[2,2,1,1] => 1600
[2,1,1,1,1] => 9375
[1,1,1,1,1,1] => 46656
[7] => 1
[6,1] => 14
[5,2] => 18
[5,1,1] => 189
[4,3] => 20
[4,2,1] => 270
[4,1,1,1] => 2240
[3,3,1] => 300
[3,2,2] => 360
[3,2,1,1] => 3200
[3,1,1,1,1] => 21875
[2,2,2,1] => 4000
[2,2,1,1,1] => 28125
[2,1,1,1,1,1] => 163296
[1,1,1,1,1,1,1] => 823543

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$F_{1} = q$

$F_{2} = q + q^{4}$

$F_{3} = q + q^{6} + q^{27}$

$F_{4} = q + q^{8} + q^{9} + q^{54} + q^{256}$

$F_{5} = q + q^{10} + q^{12} + q^{90} + q^{108} + q^{640} + q^{3125}$

$F_{6} = q + q^{12} + q^{15} + q^{16} + q^{135} + q^{180} + q^{216} + q^{1280} + q^{1600} + q^{9375} + q^{46656}$

$F_{7} = q + q^{14} + q^{18} + q^{20} + q^{189} + q^{270} + q^{300} + q^{360} + q^{2240} + q^{3200} + q^{4000} + q^{21875} + q^{28125} + q^{163296} + q^{823543}$

Description

The value of the complete homogeneous symmetric function evaluated at 1.
The statistic is

$h_\lambda(x_1,\dotsc,x_k)$ evaluated at

$x_1=x_2=\dotsb=x_k$ ,
where

$\lambda$ has

$k$ parts.

References

[1] Stanley, R. P. Enumerative combinatorics. Vol. 2 MathSciNet:1676282

Created

Jul 11, 2020 at 10:05 by Per Alexandersson

Updated

Jul 11, 2020 at 10:05 by Per Alexandersson