Ratio-Covarieties of Numerical Semigroups

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Please find comments and suggestions in the attached report.

Comments for author File: Comments.pdf

Comments on the Quality of English Language

Minor editing of English language required

Author Response

Dear Editor,

in attached file I am sending a point by point response to the reviewer's comments.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The structure of the manuscript is well done and the exposition of the arguments is sufficiently clear. The results contained in it are interesting and provide an increasing of knowledge in this area of research. Therefore, I recommend to accept the article for publication. However, I suggest the authors to fix some typos and correct some expressions. I provide, in the attached file, a list with my suggested corrections and improvements, that the authors may consider.

Comments for author File: Comments.pdf

Author Response

Thank you very much for taking the time to review this manuscript.

We agree with all the correcctions suggested by the referee and we have made them accordingly.

We have not included any reference to the set ST(F,m). The concept of Strong numerical semigroup appears only in

Robles-Pérez, A.M.; Rosales, J.C. Modular Frobenius pseudo-varieties. Collectanea Mathematica 2023, 74, 133–147

and we have had to remove this reference because the  journal policy, since the number of self-citations is limited (no more tan  20%).

 

 

Reviewer 3 Report

Comments and Suggestions for Authors

Lemma 1, Proposition 2 - give a reference or write the corresponding proof

I suggest introducing the definition of a graph as a triple (V, E, f), where f is the incidence function. Later you can then comment on what properties this graph has, since you are dealing with trees

Lemma 3 - write at least the sketch of the proof and the corresponding reference

ln 101: comment on why Proposition 4 is a consequence of Lemma 3

Lemma 8, 9; Proposition 10, 11 - give the corresponding reference and/or at least the sketch of the proof

Lemma 14, 17 - please write the corresponding proofs

Algorithm 20 - describe the algorithm in a few sentences according to the meta-language

Propositions 22 - write the corresponding reference

Corollary 26, Lemma 28 - please write the sketches of the corresponding proofs

Algorithm 30 - describe the algorithm in a few sentences according to the meta-language

Proposition 44, 47 - missing references or proofs

Lemma 49, 50, 51, 53 - missing references or proofs

 

 

Comments on the Quality of English Language

I propose a few small revisions to the text:

26 ln: The Frobenius problem (without "called")

51 ln:  "es" change to "is"

309 ln "and" in place of "y"

Please read the full manuscript and focus on the word order in each sentence.

Author Response

Dear Editor,

in attached file I am sending a point by point response to the reviewer's comments.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

See attached

Comments for author File: Comments.pdf

Author Response

Thani you very much for taking the time to review this paper. 

In attach file I am sending a point-by-point response to yours comments.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

I agree with everything that is done.

Author Response

Thank you for your review!!

 

Best Regards