would like to know the most efficient way to write a polytabloid in terms of standard ones.
I know the Garnir elements, but using them to do calculations is hard. I also read about "quadratic elements" in Fulton's Young Tableaux, but I hope a better construction exists.
The thing I would like to have is, in a perfect world, an algorithm that has a random polytabloid and a standard one as input, and the coefficient of the standard polytabloid in the expansion of the random polytabloid as an output. I don't think such algorithm exists, but it can help figure out what kind of algorithm I am looking for.