Major index of skew-SYT

asked 2019-03-19 07:29:57 -0500

joakim_uhlin gravatar image

updated 2019-03-19 10:35:37 -0500

For a standard Young tableaux (SYT), I can compute the major index as follows:

T = Tableau([[1,2,3],[4,5]])
T.major_index()

Is there a way to compute the major index of a skew-SYT currently? Something like:

S = SkewTableaux().from_expr([[1,1],[[5],[3,4],[1,2]]])
S.major_index()

At the moment, it seems major_index() is not defined for the SkewTableau-class.

EDIT: The major index of a (skew) standard Young tableau $T$, denoted $\mathrm{maj}(T)$, is defined as follows. A descent of $T$ is an entry $i$ such that $i+1$ appears strictly below $i$ in $T$. Define $\mathrm{maj}(T)$ as the sum of all descents of $T$. For example, the major index of the skew standard Young tableau above is $2+4=6$.

FindStat has a definition, although they only define it for non-skew tableau. But the definition extends trivially to skew-shapes as well.

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Comments

Can you give a reference to a (mathematical) definition?

rburing gravatar imagerburing ( 2019-03-19 10:25:50 -0500 )edit

Added the definition of major index.

joakim_uhlin gravatar imagejoakim_uhlin ( 2019-03-19 10:36:27 -0500 )edit