One variant of Fulton's K-saturation conjecture is as follows:


$K\_{\lambda/\mu,w} > 0 \Leftrightarrow K\_{n\lambda/n\mu,n w} > 0$ for any integer $n>0.$


Here $K\_{\lambda/\mu,w}$ denotes the Kostka numbers (number of skew SSYT of shape $\lambda/\mu$ and weight $w.$


This has been proved in various ways, (Knutson, Tao), so it is no longe a conjecture, but to me the proofs are quite involved. The proof shows the similar statement for Littlewood-Richardson coefficients, using K-hives and the above follows as a corollary.


**Question:** Is there an elementary proof of the above statement?
Could one expect a short proof of this?



Elementary proof of K-saturation conjecture
I answer this question [here.](http://arxiv.org/abs/1307.3999)


The proof is of combinatorial nature and quite short, using quite elementary
arguments.


