On generators of bounded ratios of minors for totally positive matrices
Abstract
We provide a method for factoring all bounded ratios of the form A(I1|I1') A(I2|I2')/ A(J1|J1') A(J2|J2') where A is a totally positive matrix, into a product of more elementary ratios each of which is bounded by 1, thus giving a new proof of Skandera's result. The approach we use generalizes the one employed by Fallat et al. in their work on principal minors. We also obtain a new necessary condition for a ratio to be bounded for the case of non-principal minors.
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