Extreme rays of the $(N, k)$-Schur Cone
Combinatorics
2016-09-06 v2
Abstract
We discuss several partial results towards proving Dennis White's conjecture on the extreme rays of the -Schur cone. We are interested in which vectors are extreme in the cone generated by all products of Schur functions of partitions with or fewer parts. For the case where , 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.
Keywords
Cite
@article{arxiv.1409.4859,
title = {Extreme rays of the $(N, k)$-Schur Cone},
author = {Christian Gaetz and Kyle Meyer and Ka Yu Tam and Max Wimberley and Zijian Yao and Heyi Zhu},
journal= {arXiv preprint arXiv:1409.4859},
year = {2016}
}
Comments
This paper has been withdrawn by the authors due to a misinterpretation of the generalized Littlewood-Richardson rule in several proofs