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Statistic identifier: St001564

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Collection: Integer partitions

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Description: The value of the forgotten symmetric functions when all variables set to 1.

Let $f_\lambda(x)$ denote the forgotten symmetric functions.
Then the statistic associated with $\lambda$, where $\lambda$ has $\ell$ parts,
is $f_\lambda(1,1,\dotsc,1)$ where there are $\ell$ variables substituted by $1$.

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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]           => 3
[3]             => 1
[2,1]           => 6
[1,1,1]         => 10
[4]             => 1
[3,1]           => 6
[2,2]           => 3
[2,1,1]         => 30
[1,1,1,1]       => 35
[5]             => 1
[4,1]           => 6
[3,2]           => 6
[3,1,1]         => 30
[2,2,1]         => 30
[2,1,1,1]       => 140
[1,1,1,1,1]     => 126
[6]             => 1
[5,1]           => 6
[4,2]           => 6
[4,1,1]         => 30
[3,3]           => 3
[3,2,1]         => 60
[3,1,1,1]       => 140
[2,2,2]         => 10
[2,2,1,1]       => 210
[2,1,1,1,1]     => 630
[1,1,1,1,1,1]   => 462
[7]             => 1
[6,1]           => 6
[5,2]           => 6
[5,1,1]         => 30
[4,3]           => 6
[4,2,1]         => 60
[4,1,1,1]       => 140
[3,3,1]         => 30
[3,2,2]         => 30
[3,2,1,1]       => 420
[3,1,1,1,1]     => 630
[2,2,2,1]       => 140
[2,2,1,1,1]     => 1260
[2,1,1,1,1,1]   => 2772
[1,1,1,1,1,1,1] => 1716

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Created: Jul 11, 2020 at 09:56 by Per Alexandersson

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Last Updated: Jul 11, 2020 at 09:56 by Per Alexandersson