ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Tue, 19 Mar 2019 13:29:57 +0100Major index of skew-SYThttps://ask.sagemath.org/question/45836/major-index-of-skew-syt/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](http://www.findstat.org/StatisticsDatabase/St000330/), although they only define it for non-skew tableau. But the definition extends trivially to skew-shapes as well.joakim_uhlinTue, 19 Mar 2019 13:29:57 +0100https://ask.sagemath.org/question/45836/