Geodesic
Dissimilarity maps on trees and the representation theory of $\mathrm{SL}_{m}(\Bbb C)$
Journal of Algebraic Combinatorics, Tome 33 (2011) no. 2, pp. 199-213.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 SL $_{ m }(\Bbb C)$.
Keywords: keywords tropical geometry, representation theory 
@article{JAC_2011__33_2_a5,
     author = {Manon, Christopher},
     title = {Dissimilarity maps on trees and the representation theory of $\mathrm{SL}_{m}(\Bbb C)$},
     journal = {Journal of Algebraic Combinatorics},
     pages = {199--213},
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     volume = {33},
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     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2011__33_2_a5/}
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Manon, Christopher. Dissimilarity maps on trees and the representation theory of $\mathrm{SL}_{m}(\Bbb C)$. Journal of Algebraic Combinatorics, Tome 33 (2011) no. 2, pp. 199-213. http://geodesic.mathdoc.fr/item/JAC_2011__33_2_a5/