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arXiv · 0903.2010

On the relation between weighted trees and tropical Grassmannians

Filip Cools
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Abstract

In this article, we will prove that the set of 4-dissimilarity vectors of n-trees is contained in the tropical Grassmannian G_{4,n}. We will also propose three equivalent conjectures related to the set of m-dissimilarity vectors of n-trees for the case m > 4. Using a computer algebra system, we can prove these conjectures for m = 5.

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Filip Cools. 2009-03-11. On the relation between weighted trees and tropical Grassmannians. https://arxiv.org/abs/0903.2010

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