multi-symmetric functions and multi-partitions
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=(x1,x2…),y=(y1,y2,…), Σ2, acts by permuting x,y. A multi-partition of a n-tuple B=(b1,…,bn) of natural numbers is a unordered set of n-tuples A1,…,Al with A1+⋯+Al=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...