Comments on "Informational laws of genome structures"

In this paper, we expose possible flaws in some of the proofs of the mathematical results presented by Bonnici and Manca, 2016 and suggest some corrected proofs of two of their results. We show that the possibility of overlap between k-mers given a fixed value of k (minimum length such that all k-mers are hapaxes) was not taken into account in several steps of the proof in Lemma 2, which makes the theorem false. For this we show a counterexample to the Lemma. In addition, we correct the proofs of Lemma 1 and Proposition 3. In the former case, we explain why the argument presented is incomplete and provide a correct proof. In the case of the latter, we show with a counter example that their claim is incorrect without explicitly mentioning the correct ranges of k over which it holds. We also provide a more general proof which accounts for this correction. We remark that although some of these comments invalidate the mathematical basis of their results, there is a possibility that the associated error becomes small in the limit n>>k, hence allowing for the apparent agreement with the data and the simulations.