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arXiv · 2204.11962

On bounded ratios of minors of totally positive matrices

Daniel Soskin·Michael Gekhtman
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Abstract

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 $\binom{2n}{n}-2n$.

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Daniel Soskin, Michael Gekhtman. 2022-04-25. On bounded ratios of minors of totally positive matrices. https://arxiv.org/abs/2204.11962

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