On the relation between weighted trees and tropical Grassmannians

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• 作者：Filip Cools
• 关键词：Weighted tree ; Dissimilarity vector ; Tropical geometry ; Grassmannian
• 刊名：Journal of Symbolic Computation
• 出版年：2009
• 出版时间：August 2009
• 年：2009
• 卷：44
• 期：8
• 页码：1079-1086
• 全文大小：600 K

文摘

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