The Schur Cone and the Cone of Log Concavity

Details The Schur Cone and the Cone of Log Concavity The Schur Cone and the Cone of Log Concavity

2009-03-16

arxiv.org/abs/0903.2831v1

Mathematics

Combinatorics

11 pages

Scientific paper

Let $\{h_1,h_2,...\}$ be a set of algebraically independent variables. We ask which vectors are extreme in the cone generated by $h_ih_j-h_{i+1}h_{j-1}$ ($i\geq j>0$) 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.

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