The minimum value of the Colless index

03/27/2019

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by   Tomás M. Coronado, et al.

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The Colless index is one of the oldest and most widely used balance indices for rooted bifurcating trees. Despite its popularity, its minimum value on the space T_n of rooted bifurcating trees with n leaves is only known when n is a power of 2. In this paper we fill this gap in the literature, by providing a formula that computes, for each n, the minimum Colless index on T_n, and characterizing those trees where this minimum value is reached.