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I'm currently writing a paper of my results in a field of pure mathematics.

My work is a generalization of an already existing result, which is not mine. My adviser and I think that there is a substantial differences between my result and the already existing result, and so it's worth a publication.

Since I'm generalizing an already existing paper it will be very convenient both for me and the readers that I will use the same notations and definitions as in the other paper. So I wrote those down and cited the other authors.

The part of definitions and notations is roughly 10%-15% of the whole paper, and even though I properly cited the other authors, I'm worried to be accused of plagiarism by the "automatic plagiarism detector", which I heard most journals use.

How can I avoid being falsely accused for plagiarism?

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    "We follow the notation and conventions of [ref], reviewed below for ease of reference." or something along those lines? – starless Apr 13 '18 at 9:40
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    @starless yes this is exactly what I've done. Is it enough to ensure that an automatic machine (not a human-being) won't accuse me for plagiarism. – Yanko Apr 13 '18 at 9:42
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    I agree with David that you should write things in your own words, but this might admittedly easily lead to very similar passages if the text is very maths-heavy, since there is usually a rather rigid way of doing things. Usually those automated machines are bad at distinguishing anything mathy, so I'd imagine you'd be safe. – starless Apr 13 '18 at 10:56
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    I don't believe that such a plagiarism detector is used in math: academia.stackexchange.com/a/82056/19607 – Kimball Apr 13 '18 at 14:32
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    The plagiarism detector is usually a first step to flag for human review, often presenting the submission alongside what it might be plagiarizing from. If you've properly cited your sources and added a contribution beyond what came before, a human reviewer/editor should be able to see that, and dismiss any flag as a false positive. – WBT Apr 14 '18 at 15:03
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It is generally known that definitions and restated theorems can cause significant textual overlap between papers to an extent that could be considered problematic. There is no point in worrying about automatic plagiarism checks for journal submissions: If a journal is relying on that alone without an editor checking, it is not a reasonable journal to submit to anyway.

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    Thank you, and what about the arXiv? are they solely relying on these programs? – Yanko Apr 13 '18 at 11:53
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    The arXiv runs an automated tool that will add a note to your article regarding its findings. For how that works, and how to deal with it, asking a separate question might be the way to go. – Arno Apr 13 '18 at 13:01
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Don't copy that part of the other paper word-for-word. Just introduce the notations and definitions in your own words.

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  • Thanks for the advice, follow up question: Is it okay to cite their paper and then write it in my own words? Also I'm not quit sure how those automatic programs work, should I completely change the sentence or just change few words? – Yanko Apr 13 '18 at 9:58
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    @Yanko There is some kind of misunderstanding. "Writing in your own words" doesn't mean that you copy something and then change it a bit. It really means that you write it yourself. Put aside whatever original paper you have been reading. Don't look at it. Imagine you explained the key definitions to a colleague with a whiteboard; how would you do it? Now do the same thing in writing. Start writing, without looking at the source; explain the definitions in a way that works best for you. It should be a story that you tell, not something you copied and edited a bit to obfuscate similarities. – Jukka Suomela Apr 13 '18 at 10:40
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    @JukkaSuomela: "Put aside whatever original paper you have been reading. Don't look at it." - from the point of view of avoiding accusations of plagiarism, this may be good advice. For the content of the paper, however, it may not: Assuming the original work was of a high quality, not looking at its definitions sounds like a recipe for forgetting about some corner case that may have been covered in the original text. – O. R. Mapper Apr 13 '18 at 11:49
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    @O.R.Mapper Of course you will double-check every detail once you have prepared the first draft of your own text, and at that point compare everything with the original if needed. – Jukka Suomela Apr 13 '18 at 11:58
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    @O.R.Mapper I read that as "Read the paper, understand it, then put it aside and rewrite without looking at it", which is much more reasonable than "guess what the paper says without ever reading it". – Fund Monica's Lawsuit Apr 13 '18 at 17:09
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It becomes plagiarism only if you intentionally present [parts of] someone else's work as your own, otherwise it is citation. Robots may not be smart enough to distinguish, but that's why nobody relies on them much: they help to make decisions, not make decisions by themselves. What those automatic systems do is mark parts of your work as resembling parts of some other works to attract attention of human reviewers, who decide if that is plagiarism or not. Don't bother rephrasing the quotes just to game those systems.

I saw one of such systems at work, it would paint shorter indirect quotes yellow, indicating it has "79% overlap with [7]", a long direct quote it would paint red, because it's "100% overlap" with [19]", then add something like another "References" section, where those [7] and [19] would be, so the reviewers can examine them, if they want. Would be no problem for you if you made it clear that those are quotes and provided the references. (Also, it painted the entire "Reference" section red, because every reference was already used in like 200 other papers, but of course nobody takes that as plagiarism.)

The reviewers may still reject the paper because it has "too much quotations/too little original content", but that's a different story.

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  • Great point about how these systems work. I have also used a system that works as you describes (for student papers), and a journal editor should not be confused when seeing these results and reading the attributions in the paper. – cactus_pardner Apr 13 '18 at 17:15
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If it is your formula, then I would think you would be safe. You have cited those that you took directly from others. Also, some may be so generic that they don't need citing, such as 'E=MC Squared'that obviously came from Einstein but it is so well known it doesn't need to be cited.

In my experience, when I write a paper it is usually tagged by some percentage as plagiarized. Once as high as 15%, and when I checked the sources, I was one of the people who I plagiarized. Those automatic, computer-generated, reports are very inaccurate to a degree, so I wouldn't worry about it. If you genuinely think it is a problem, talk to your professor, advisor, or publisher.

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What you don't want to do — is to copy their definitions exactly. Even though you are in pure mathematics, definitions, phrasings, and explanations can and should be different. Moreover, in a paper, the things are introduced in a specific order – and I doubt that you have exactly the same focus as the previous paper. Thus, even a very similar section with the definitions & notations will be different.

I also suggest to include in the paper:

  • in the introduction: the sentence/paragraph that highlights the connection (problem statement, similarity, differences) between yours and the original paper
  • in the main part: the sentence that discloses using the same notations as in [1].
  • possibly in the submission itself (if allowed): a PDF of the preceding paper that has to be read by peers to judge the novelty of this publication and how it extends the obtained results.

In general, for peer review in a reputable journal, you should not be afraid of automatic machines too much. Especially, if you/your advisor have a history of publications in this journal/field and good reputation. Also, if you follow the general guidelines for "writing in your own words for your own paper goals", you should automatically pass even the strictest automatic machines.

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    I strongly disagree with the first two sentences. Sometimes, one can reasonably adapt notation to different purposes, or clear stuff up or otherwise make sensible changes to definitions. Sometimes, one cannot, and rephrasing for the sake of it is a bad idea. – Arno Apr 13 '18 at 10:28
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    @Arno Even if your definitions and notation are identical, it's rare that if you wrote the sentence yourself without literally copy/pasting the definition, then you would use the exact same words. I mean, try to write the definition of a group, and compare your phrasing with Wikipedia, for example – I doubt it will be identical, but the definition is the same... – user9646 Apr 13 '18 at 10:42
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    @Arno you certainly have a point, rephrasing for the sake of rephrasing is a bad idea. However, I cannot believe that one will not feel the need to reorganize/rephrase/restructure a big part of the paper that will cause the automatic checker to scream. The question if automatic checking is even an issue – is different, and here I totally agree with your answer. – Anton Menshov Apr 13 '18 at 10:43

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