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About a year ago, I published a paper. Since then, through discussions with some colleagues, we have identified several interesting corollaries that can be derived from its results, with only minor adaptations to the proofs. These corollaries appear to be particularly relevant to a scientific community that is relatively distinct from the one targeted by the original paper.

In this context, would it be reasonable to write a new paper presenting these corollaries, highlighting their relevance in this new framework, and submit it to a journal that caters more specifically to this other community?

My main concern is that this might be perceived as "salami slicing," since the proofs rely on very similar arguments to those in the original paper. Are there cases where such papers, building on an earlier work, are considered interesting and legitimate to publish?

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    $\begingroup$ Stop worrying about how your actions are perceived and start doing the right things. $\endgroup$
    – Algernon
    Commented Nov 26 at 13:16
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    $\begingroup$ I agree with Algernon. If your motives are good then you should proceed as you see fit, and ignore the "haters." By the way, Gian-Carlo Rota actually says it is good practice "to present the same result in several versions, each one accessible to a specific group." $\endgroup$
    – Timothy Chow
    Commented Nov 26 at 18:07
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    $\begingroup$ I understand Algernon's point, but I often wonder what criteria determine whether something is worth publishing. It’s interesting to hear others’ perspectives on papers that are enlightening but not necessarily original. By the way, the Riesz example mentioned by Gian-Carlo Rota is a great illustration. $\endgroup$
    – BabaUtah
    Commented Nov 26 at 18:45
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    $\begingroup$ @BabaUtah Journal referees determine whether or not something is worth publishing. If your result is useful, they will most likely acknowledge it. If it is not, they will inform you of it. $\endgroup$
    – paulina
    Commented Nov 27 at 17:47
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    $\begingroup$ @paulina, re, referees offer an opinion on whether something is worth publishing, and, though it is the editorial board that makes the decision, can even be said (nearly) to determine whether or not something is published, but I think it is putting it too strongly to say that we determine whether something is worth publishing. We definitely get it wrong, both ways! $\endgroup$
    – LSpice
    Commented Nov 28 at 0:44

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There is a famous paper where the main result is derived as a simple corollary of a result of another author published 23 years before:

J. Milnor, Eigenvalues of the Laplace operator on certain manifolds, Proc. Nat. Acad. Sci. U.S.A. 51 (1964), 542.

The whole paper, with introduction and reference list occupies less than 1 page.

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    $\begingroup$ Similarly, in R. Stanley, The number of faces of a simplicial convex polytope, Advances in Math. 35 (1980), 236-238 (math.mit.edu/~rstan/pubs/pubfiles/46.pdf), Stanley proves McMullen's g-conjecture characterizing $f$-vectors of simplicial polytopes in two pages, basically as a corollary of known facts about toric varieties and their cohomology, Hard Lefschetz, etc. $\endgroup$
    – Sam Hopkins
    Commented Nov 26 at 15:35
  • $\begingroup$ That's great examples ! thanks. $\endgroup$
    – BabaUtah
    Commented Nov 26 at 18:48
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In general, the rule is that one may (but not necessarily should) publish everything he/she considers worth attracting people's attention to (under the condition that their attention is not there already). On the other hand, I usually prefer to disseminate the new results and ideas I have (if I have any, which is a more and more seldom event) among a few experts and colleagues before even writing the full details down to see if there is any interest in them (if there is none, it spares me a lot of time and effort), so if you have some target audience in mind, I would choose a few names out of that list and communicate to them first. If you see a lot of excitement, by all means prepare a detailed article and submit to some visible journal. If you are met with total indifference, just post a short note on arXiv and stop there.

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    $\begingroup$ I upvoted this answer. At the same time, I personally would err on the side of trying to publish. It's possible that you have bad luck, and the few people you pick are not interested, yet someone else that you did not ask is very interested. $\endgroup$
    – Timothy Chow
    Commented Nov 27 at 14:36
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    $\begingroup$ @TimothyChow You are absolutely correct, but imagine all that writing, 5 rounds (minimum) of painstaking proofreading, dealing with referee reports (especially when they start talking about their great ideas of how the introduction should be written, whom I should cite, etc. instead of the real meat), etc., etc. Brr--rr--rrr. I'm lazy (plus also old now), so if I have a good pretext to squiggle out of it, I usually do. :-) $\endgroup$
    – fedja
    Commented Nov 27 at 21:46
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IMO, no problem at all. Say, our results on the congruence speed of tetration come from 5+ years of research, and the final formula of the constant congruence speed of tetration invokes a previously published paper, which extended an earlier paper of mine.
You could call the new results Theorems if they are relevant and their proof is still nontrivial even after you invoke the previously published theorems. Otherwise, I would explain what you have written here in the introduction of the new paper.

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  • $\begingroup$ In the end, I’d probably lean toward the second option: explaining why I think such results deserve their own papers in introduction. $\endgroup$
    – BabaUtah
    Commented Nov 26 at 18:52
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To avoid salami-slicing, just keep the size and claims of the new paper appropriately modest. The problematic sense of salami-slicing is when a twenty-page paper appears to claim complete novelty, but closer inspection reveals that eighteen of those pages are essentially recycling earlier work. The examples in Alexandre Eremenko’s answer and its comments avoid that by staying very short and sweet, giving just the new results, which is excellent when it fits the audience. If you’re targeting the corollary-paper at a different subfield, then that may not be suitable — you may well want to re-capitulate the earlier work with an adapted presentation — so then be clear up-front in the abstract about how much novel substance there is: “It turns out that the widget-theoretic results of [XYZ, 2023] also have new implications for gizmos. In this paper we recall the earlier results from a more gizmo-theoretic perspective, and present the new applications, which are relatively straightforward corollaries.”

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    $\begingroup$ Pah, gizmo theory is a fad. $\endgroup$
    – LSpice
    Commented Nov 28 at 0:45

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