The Schur Cone and the Cone of Log Concavity
| Autor: | White, Dennis E. |
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| Rok vydání: | 2009 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 11 pages Corrected proof of Littlewood-Richardson identity; added new material on Littlewood-Richardson identity; removed some extraneous material and moved some sections |
| Databáze: | arXiv |
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