Hope that the following soft question is still appropriate on MathOverflow. I was wondering if there is any communal protocol or etiquette with regard to the resubmission of a research paper after it has been superseded by another as yet unpublished paper.
Here's the situation in detail. Suppose that a paper of yours, call it paper A, regarding the existence of some mathematical object foobar has been rejected by some journal X. Before you received the news of rejection of paper A by journal X, you obtained bounds on the complexity of foobar and submitted these complexity estimates as paper B to journal Y. Given that paper B is still pending the refereeing process, would you resubmit paper A to another journal X'? Is it unethical to do so?
Of course, one question is what is the worth of paper A, given that it has been superseded by paper B. One possible factor to take into consideration is that paper B is substantially longer than paper A (in my case paper B about 40 pp. and paper A is about 20 pp.). There may be readers interested in the existence argument of paper A without bothering about the complexity estimates in paper B.
Best Answer
This is a tricky situation, though just one spin off of the current absurd state of academic publishing, and particularly the preposterously slow and uneven peer review process in math. My personal feeling is that you should try about as hard to get paper A published as you would any other paper (though strategically, I would probably submit to a somewhat less selective journal). It does feel a little silly; I actually now am in the doubled version of this situation, where I wrote a paper, wrote another that superseded it, and then wrote another that superseded that one, all of which are under review simultaneously at the moment. The process in mathematics has gotten a bit silly just generally, but any reason you had to publish paper A before (whether it is padding your CV, making sure that it is regarded as a reliable part of the peer reviewed literature, or hoping to get useful feedback from a referee) is equally in force now, so I don't see what has really changed.