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CompleteHomogeneousSymmetricFunctionAtOne on IntegerPartition ​

The complete homogeneous symmetric function indexed by the partition, in as many variables as it has parts, all set to 1: the product of the multiset coefficients of the number of parts and each part.

On IntegerPartition

Called as CombinatorialStat(x, "CompleteHomogeneousSymmetricFunctionAtOne"). The head's page has its examples.

Live

Distribution

Over IntegerPartitions at each size, tallied here in your browser; sizes past 30 are not offered.

FindStat St001562

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

ObjectValue
[1]1
[2]1
[3]1
[4]1
[5]1
[6]1
[7]1
[1,1]4

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001562 has the rest.