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Some time ago I wrote a preprint (this one: http://arxiv.org/abs/1002.2651) that contains one main result (Theorem 2.2.1(1)) and several applications for it. Most of the applications could be deduced from the main result automatically using the methods developed in my previous papers.

Now I submitted the preprint, and the referee says: the main result is quite nice, but he does not want me to repeat much of the previous papers; so I should make the 'applications' part much shorter. I don't object against making the paper shorter; yet a reader that knows nothing about my previous work will probably not understand why the main result is important. So, I would like to mention the applications somehow.

Now my main question is: what could be the best way to do this? The referee wants the paper to be really short; so is it reasonable to make a list of applications and ask the readers to read the details in the references? Can I make a reference to the preprint version of the paper (which would be longer)?

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I once wrote a paper with Frank Calegari, containing a chapter which was standard proofs of "well-known" results for which we could find no reference. The referee didn't like this chapter. So we removed it and resubmitted, and I put both versions on my web page. –  Kevin Buzzard Oct 27 '10 at 13:38
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My answer to your last question is "yes". Specifically, I think it should be ok to do the following:

  • Extend your arXiv preprint to fill it out with even more details of the applications, to provide a potential reader with the background that you have in mind; and

  • In the submitted version, just cite the arXiv version of the paper by saying something like: "...for further motivation and examples of applications to X, Y, and Z, we refer the reader to the companion report~\cite{arXiv}"

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I agree: I have seen this in papers in print before (unfortunately I don't recall where) and I think it is quite helpful to the interested reader. –  Pieter Naaijkens Oct 27 '10 at 12:20
    
So, do you think that journals and referees usually do not object against this? Then I will probably so; thanks! –  Mikhail Bondarko Oct 27 '10 at 12:36
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I've done this on about half of my papers. Many referees seem to think that I write too many details. I'm from the school of thought that: the more details there are, the easier for the reader to understand. The reader can always skip details if they're not interested. So I have several papers which mention something like "a longer, more detailed version of this paper can be found on the arXiv." Actually, I hope most people read the arXiv versions of my papers rather than the published versions. I also prefer my own margins, spacing, and formatting to most journal styles. –  Spiro Karigiannis Oct 27 '10 at 13:03
    
I should add that I suppose trimming a paper's length is important for journals which still publish in print form, although doing so at the expense of clarity is not something I agree with. However, for electronic-only journals, I really can't see why anyone would complain that an article is better to be shorter than to be clearer. Again, people don't have to read it all! –  Spiro Karigiannis Oct 27 '10 at 13:04
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@Mikhail, re: your question to Pieter -- presumably you could ask the editor to pass that question to the referee for you, no? (I mean, I don't know if this is standard practice, but it seems like it shouldn't be too much trouble to ask for clarification on such a point from the person who made the original comment.) –  JBL Oct 27 '10 at 13:21
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