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It is well known that in a binary tree the external path length minus theinternal path length is exactly 2n-2, where n is the number of external nodes.We show that a generalization of the formula holds for compacted tries,replacing the role of paths with the notion of extent, and the value 2n-2 withthe trie measure, an estimation of the number of bits that are necessary todescribe the trie.

E = I + T: The internal extent formula for compacted tries