DualImmaculateMonomialColumnSum on IntegerComposition

The sum of the entries in the column of the composition in the matrix from the dual immaculate to the monomial quasisymmetric functions.

On IntegerComposition

FindStat's St000817: the number of immaculate tableaux of the shape with any gapless content (Berg, Bergeron, Saliola, Serrano and Zabrocki).

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

Live

Distribution

Over IntegerCompositions at each size, tallied here in your browser; sizes past 6 are not offered.

Sizes 1 to

FindStat St000817

The sum of the entries in the column specified by the composition of the change of basis matrix from dual immaculate quasisymmetric functions to monomial quasisymmetric functions.

Object	Value
[2]	2
[3]	4
[4]	8
[5]	16
[6]	32
[7]	64
[8]	128
[9]	256

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000817 has the rest.