Dissimilarity maps on trees and the representation theory of SLm(ℂ)
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- Manon, C. J Algebr Comb (2011) 33: 199. doi:10.1007/s10801-010-0241-9
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We prove that m-dissimilarity vectors of weighted trees are points on the tropical Grassmannian, as conjecture by Cools in response to a question of Sturmfels and Pachter. We accomplish this by relating m-dissimilarity vectors to the representation theory of SLm(ℂ).