The Schur Cone and the Cone of Log Concavity

Abstract

Let $\{h_1,h_2,...\}$ be a set of algebraically independent variables. We ask which vectors are extreme in the cone generated by $h_i{h}_j-h_{i+1}{h}_{j-1}$ ($i\ge j>0$) and $h_i$ ($i>0$). We call this cone the cone of log concavity. More generally, we ask which vectors are extreme in the cone generated by Schur functions of partitions with $k$ or fewer parts. We give a conjecture for which vectors are extreme in the cone of log concavity. We prove the characterization in one direction and give partial results in the other direction.

11 pages Corrected proof of Littlewood-Richardson identity; added new material on Littlewood-Richardson identity; removed some extraneous material and moved some sections

Cited by in corpus (1)

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