Geodesic
Dissimilarity Vectors of Trees and Their Tropical Linear Spaces (Extended Abstract)
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011) (2011).

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We study the combinatorics of weighted trees from the point of view of tropical algebraic geometry and tropical linear spaces. The set of dissimilarity vectors of weighted trees is contained in the tropical Grassmannian, so we describe here the tropical linear space of a dissimilarity vector and its associated family of matroids. This gives a family of complete flags of tropical linear spaces, where each flag is described by a weighted tree. 
@article{DMTCS_2011_special_260_a31,
     author = {Iriarte Giraldo, Benjamin},
     title = {Dissimilarity {Vectors} of {Trees} and {Their} {Tropical} {Linear} {Spaces} {(Extended} {Abstract)}},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011)},
     year = {2011},
     doi = {10.46298/dmtcs.2918},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2918/}
}
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Iriarte Giraldo, Benjamin. Dissimilarity Vectors of Trees and Their Tropical Linear Spaces (Extended Abstract). Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011) (2011). doi : 10.46298/dmtcs.2918. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2918/

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