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The following item appears in the $\LaTeX$ style-guide for the Journal of Integer Sequences: JIS excerpt

To me this seems correct and reasonable, but it in most articles I read, authors tend toward the first example of "wrong" usage. Is this simply journal-specific, or is it abusive to use "In [1]..."?

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    $\begingroup$ I will go even farther and say that in my opinion there's nothing wrong with using a citation number as an object of a preposition. $\endgroup$ – Ira Gessel Oct 5 at 17:43
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    $\begingroup$ This seems like fussy advice. [1] stands for "Adler - Refined anisotropic K-types" (in most of my papers, anyway); setting up this correspondence is what the bibliography is there to do. Thus, "In [1] …" means "In Adler - Refined anisotropic K-types …", which is very near being perfectly grammatical. Let anyone who has a problem with it fuss over splitting infinitives instead. $\endgroup$ – LSpice Oct 5 at 18:02
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    $\begingroup$ In my experience, these journal style guides are largely ignored. $\endgroup$ – Federico Poloni Oct 5 at 19:31
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    $\begingroup$ I think this style guide instruction is unacceptably pedantic. $\endgroup$ – David Handelman Oct 6 at 0:36
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    $\begingroup$ I always use the "wrong" variant, as it seems the only grammatically reasonable thing to do. Why would one write something that is treated like footnotes not as footnotes? $\endgroup$ – Fred Rohrer Oct 6 at 4:39
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I don't think this kind of thing is "abusive." I'm certain I've done it in my own writing before, and I can think of several scenarios where it's better than the alternative:

(1) If a citation has no author, like a collaboratively edited industry standard for some software.

(2) If a citation has many authors and it's awkward to write "Smith, et. al. proved ... [1]"

(3) If a citation is an edited volume and it's unclear who contributed the thing you need to cite.

Generally, I think the guiding principle should be to do whatever will make your writing easier for the reader. It seems to me that there are many times when the reader just needs to know the result and which citation they should look it up in, rather than who was the first author on the paper where that result appears. Much more important to me than the question of whether I write "In [1], the authors prove..." instead of "So and so proved ... [1]" is that the citation contain a more precise reference, like Theorem 5.3.2 instead of just citing a 1000 page book and leaving the reader to go hunting for the result.

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    $\begingroup$ +1000 for your last sentence! $\endgroup$ – Jochen Glueck Oct 5 at 18:00
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    $\begingroup$ A favourite of mine is to find out that [1] is a citation to all 10 parts of a 10-part paper. This is bad enough when done by someone else, but when done by the author of those papers who should know (or be able to grep the TeX of) the contents, it is downright annoying. (It's better than "the result is well known", at least.) $\endgroup$ – LSpice Oct 5 at 18:04
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    $\begingroup$ I just checked a few pages from one of my own papers and found that about half of the citations there are "wrong". So "wrong" must not really be wrong. $\endgroup$ – Andreas Blass Oct 5 at 18:39
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    $\begingroup$ I also would like to mention that using the name of the first author is annoying for the alphabetically challenged among us... $\endgroup$ – Denis Nardin Oct 6 at 16:05

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