multi-symmetric functions and multi-partitions

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Does sage support manipulating multi-symmetric functions/polynomials and/or multi-partitions? Multi-symmetric functions are like the usual symmetric ones, except the symmetric group acts by permuting "vectors" of variables simultaneously, e.g. for an two vectors $x=(x_1,x_2\dotsc), y=(y_1,y_2,\dotsc)$, $\Sigma_2$, acts by permuting $x,y$. A multi-partition of a $n$-tuple $B=(b_1,\dotsc,b_n)$ of natural numbers is a unordered set of $n$-tuples $A_1,\dotsc,A_l$ with $A_1 + \dotsm + A_l = B$.

I'd like to have a combinatorial class of multi-partitions with similar functionality as partitions, e.g. .first(), .last() methods and iter(). I'd also like to have a class like SymmetricFunctionAlgebra, but with multi-symmetric functions instead. I've had a bit of a poke around and there's some functionality in Maxima (in the Sym) package that might help, but not quite like what I want (that I can find). So, before writing code, I'm asking here.

If the code needs to be written, I'm quite keen to make it my first (hopefully of many) contribution to sage...

asked Nov 11 '10

Paul Bryan gravatar image Paul Bryan
31 1 1

updated Apr 28 '11

Kelvin Li gravatar image Kelvin Li
453 1 10 17
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I don't think that what you want is available directly in sage, although there may be some tricks available depending on exactly what you want to do. I don't have time to go into more depth right now, but please post this question to the Google Group: sage-combinat-devel. There are a lot of people (including me!) who read that, who would be interested in getting this kind of functionality into sage.


posted Nov 12 '10

Jason Bandlow gravatar image Jason Bandlow
381 1 8 18

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Asked: Nov 11 '10

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