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Statistic identifier: St001562

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Collection: Integer partitions

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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.

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

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Code:


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Statistic 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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Created: Jul 11, 2020 at 10:05 by Per Alexandersson

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Last Updated: Jul 11, 2020 at 10:05 by Per Alexandersson