Extreme rays of the $(N,k)$-Schur Cone

Abstract

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.

This paper has been withdrawn by the authors due to a misinterpretation of the generalized Littlewood-Richardson rule in several proofs

References in corpus (1)

• The Schur Cone and the Cone of Log Concavity