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A positive part can be defined for each of the $(n-1)!/2$ possible planar orderings, $\\alpha$, and agrees with the corresponding planar trees in the moduli space, ${\\rm Trop}^{\\alpha}G(2,n)$. Motivated by a physical application we study the way ${\\rm Trop}^{\\alpha}G(2,n)$ and ${\\rm Trop}^{\\beta}G(2,n)$ intersect in ${\\rm Trop}\\, G(2,n)$. 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