Nonnegative Laurent expansion conjecture for minors and chamber minors

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Let MM be a generic square matrix, and let a double wiring diagram be arbitrary. The chamber-minor Laurent positivity conjecture. Every minor of MM can be written as a Laurent polynomial with nonnegative integer coefficients in the chamber minors of the diagram.

This refines the known result that every minor has a Laurent-polynomial expression with integer coefficients in the chamber minors. The conjecture strengthens that statement by requiring coefficientwise nonnegativity for every double wiring diagram.

References

Primary source

Sergey Fomin and Andrei Zelevinsky, “Total positivity: tests and parametrizations”, arXiv:math/9912128 (1999).

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