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 2 ≤ m ≤ n, 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.

Bocci, C., Cools, F. (2009). A tropical interpretation of m-dissimilarity maps. APPLIED MATHEMATICS AND COMPUTATION, 212(2), 349-356 [10.1016/j.amc.2009.02.031].

### A tropical interpretation of m-dissimilarity maps

#### Abstract

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 2 ≤ m ≤ n, 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.
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2009
Bocci, C., Cools, F. (2009). A tropical interpretation of m-dissimilarity maps. APPLIED MATHEMATICS AND COMPUTATION, 212(2), 349-356 [10.1016/j.amc.2009.02.031].
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11365/21087`