A tropical interpretation of m

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• 作者：Cristiano Bocci ; Filip Cools
• 关键词：Tree ; Dissimilarity map ; Tropical geometry ; Grassmannian
• 刊名：Applied Mathematics and Computation
• 出版年：2009
• 出版时间：15 June 2009
• 年：2009
• 卷：212
• 期：2
• 页码：349-356
• 全文大小：201 K

文摘

Let T be a weighted tree with n numbered leaves and let D=(D(i,j))_i,j be its distance matrix, so D(i,j) is the distance between the leaves i and j. If m is an integer satisfying 2mn, we prove a tropical formula to compute the m-dissimilarity map of T (i.e. the weights of the subtrees of T with m leaves), given D. For m=3, we present a tropical description of the set of m-dissimilarity maps of trees. For m=4, a partial result is given.