ASKSAGE: Sage Q&A Forum - Latest question feedhttp://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Tue, 19 Mar 2019 07:29:57 -0500Major index of skew-SYThttp://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 07:29:57 -0500http://ask.sagemath.org/question/45836/how to define Skew Polynomial Ring over Cyclotomic Fieldhttp://ask.sagemath.org/question/40199/how-to-define-skew-polynomial-ring-over-cyclotomic-field/how to define Skew Polynomial Ring in x over Cyclotomic Field of order 7 and degree 6 twisted by zeta7 |--> zeta7^2
when i execute those commands
K = CyclotomicField(7)
sigma = K.hom([K.gen()^2])
S.< x > = K['x',sigma]
I have this message error
> AssertionError: coercion from
> Cyclotomic Field of order 7 and degree
> 6 to Skew Polynomial Ring in x over
> Cyclotomic Field of order 7 and degree
> 6 twisted by zeta7 |--> zeta7^2
> already registered or discoveredBouzidi AhmedSun, 17 Dec 2017 04:36:39 -0600http://ask.sagemath.org/question/40199/