- FindStat

Identifier

St001564: Integer partitions ⟶ ℤ

Values

=>
                            Cc0002;cc-rep
                            
                            
                            

                        [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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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 $1$.

References

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

Created

Jul 11, 2020 at 09:56 by Per Alexandersson

Updated

Jul 11, 2020 at 09:56 by Per Alexandersson