On bounded ratios of minors of totally positive matrices

2022/04/25 by Soskin, Daniel, Gekhtman, Michael · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2204.11962

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 \binom2nn-2n.

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