Nonnegative Laurent expansion conjecture for minors and chamber minors
Let be a generic square matrix, and let a double wiring diagram be arbitrary. The chamber-minor Laurent positivity conjecture. Every minor of 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).
Progress summary
Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.
Solutions 0
No solutions have been posted yet.