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.Thu, 11 Apr 2019 02:56:49 -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/Setting t=0 in a non-symmetric E-Macdonald polynomialhttp://ask.sagemath.org/question/46090/setting-t0-in-a-non-symmetric-e-macdonald-polynomial/ Suppose I have a non-symmetric [E-Macdonald polynomial](https://arxiv.org/abs/math/0601693) indexed by, say, $\mu=(0,1,1)$. Then I can write
from sage.combinat.sf.ns_macdonald import E
E([0,1,1])
and I get a polynomial in three variables and with coefficients in $\mathbb{Q}(q,t)$:
((-t + 1)/(-q*t + 1))*x0*x1 + ((-t + 1)/(-q*t + 1))*x0*x2 + x1*x2
However, I am confused about how I can work with this polynomial. For my purposes, I would like to study the specialization $t=0$. It would be really neat if there were some way to get write something like
Epoly(x_0,x_1,x_2,q,t) =...
so I could easily specialize variables as I go along.
joakim_uhlinThu, 11 Apr 2019 02:56:49 -0500http://ask.sagemath.org/question/46090/