  We discuss several partial results towards proving Dennis White's conjecture
on the extreme rays of the $(N,2)$-Schur cone. We are interested in which
vectors are extreme in the cone generated by all products of Schur functions of
partitions with $k$ or fewer parts. For the case where $k =2$, White
conjectured that the extreme rays are obtained by excluding a certain family of
"bad pairs," and proved a special case of the conjecture using Farkas' Lemma.
We present an alternate proof of the special case, in addition to showing more
infinite families of extreme rays and reducing White's conjecture to two
simpler conjectures.
