Is it reasonable to submit a paper to a journal that I have uploaded to the Arxiv 4 years ago?

Question

I have a paper submitted to the Arxiv 4 years ago (with another co-author). At that time, the only reason that we put the article online was that someone asked us to do that in order to cite it. Since then it has been cited some times, including authors that claim that have found (independently) the same proof as ours. The paper is the solution of a combinatorics problem.

I have been thinking lately that it would help my career to get this paper published in a Journal, but I'm not quite sure if this is a good idea, since it is certainly not a new result (and it is not super-interesting, just a nice solution for a problem).

What should I do? Has anyone been in the same situation?

Any advice is very welcome!

PS: In case that is a good idea to get it published it would be nice to have some kind of advise of which journal might consider articles of the types I described, as I guess that lots of Journals won't even consider it.

Answer 1

In math, it commonly happens that, for whatever reason, an unpublished work gets cited several times. (This is rather annoying when it is something useful but not easily accessible, though this is not quite your case.)

I think that whether you can easily publish it depends on how similar the work is now to published work. A collaborator and I were in a somewhat similar situation (though not the same), but our focus was different and we discussed some different things so it was publishable. (He didn't think it was interesting enough to publish originally many years ago, but then we did some additional things that made it more interesting, even after someone else had published the main result with the same method independently.)

If you want to publish it, here are two suggestions: 1) try to publish as is in conference proceedings, or 2) incorporate your old paper into a new paper which does some other things (it could be expository, or with additional new research).

As for whether publishing it will help your career, my guess it won't make a huge difference, unless you only have 1 or 2 publications, though it may help some. (It's not likely to get into a top journal unless you do something else.) It sounds like people know about your work, so letter writers can talk about it if they think it's important (in which case maybe you should've published it! but one doesn't always know in advance what will be interesting), and on your CV you can always list it as a preprint.

Answer 2

I would attempt placing it in a journal. You did the work and I'm assuming you came up with the first, greatly improved proof. You also have citations so it must be important to someone other than you.

Answer 3

You say that the result is "not new" and "not super interesting", so I'm not sure why it should be published in any event, regardless of whether or not and when it appeared on the arXiv.