We prove the following formula: Proof: Let g ∈ S * be a n-gram in the reference summary, and k ∈ [1, m] the number of sentences in which it appears.
in order to prove the formula (20), we have to find an expression for the (k) that gives to g the correct contribution to the formula: First, we observe that g does not appear in the terms that contain the intersection of more than k sentences.