论文标题
完全矩阵的未成年人的有限比率
On bounded ratios of minors of totally positive matrices
论文作者
论文摘要
我们提供了几个完全正面基质的未成年人的有界劳伦的单元的例子，这些矩阵的未成年人无法将其纳入所谓的原始比率的产物，从而表明，关于Fallat，Gekhtman和Johnson在[3]中所述的有界比率分解的猜想是对界限的分解。但是，所有发现的例子都满足了[3]中所述的无减法猜想。此外，我们表明所有有界比率的集合形成了尺寸的多面体锥$ \ binom {2n} {n} -2n $。
We provide several examples of bounded Laurent monomials of minors of a totally positive matrix, which can not be factored into a product of so called primitive ratios, thus showing that the conjecture about factorization of bounded ratios stated in [3] by Fallat, Gekhtman, and Johnson does not hold. However, all found examples satisfy subtraction-free conjecture stated also in [3]. In addition, we show that the set of all bounded ratios form a polyhedral cone of dimension $\binom{2n}{n}-2n$.
