Benjamin Iriarte Giraldo - Dissimilarity Vectors of Trees and Their Tropical Linear Spaces (Extended Abstract)

dmtcs:2918 - Discrete Mathematics & Theoretical Computer Science, January 1, 2011, DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011) - https://doi.org/10.46298/dmtcs.2918
Dissimilarity Vectors of Trees and Their Tropical Linear Spaces (Extended Abstract)Article

Authors: Benjamin Iriarte Giraldo 1

  • 1 Department of Mathematics [MIT]

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.

https://doi.org/10.46298/dmtcs.2918
Source: HAL:hal-01215099v1
Volume: DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011)
Section: Proceedings
Published on: January 1, 2011
Imported on: January 31, 2017
Keywords: dissimilarity vector,tropical linear space,tight span,weighted tree,matroid polytope,T-theory,[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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