Are there any restrictions on applying to the same graduate school in two consecutive years? I have the following dilemma: I am finishing my Master's degree in pure mathematics this academic year (summer 2015) and I hoped to apply to a PhD program (US schools) starting from September 2015. Therefore, I have to apply this fall (till December 2014 in most places).

However, I have the following problem - my first article has just been completed and I have to go through a painful publication process which will not be finished in time (surely not till December). Second problem is that I have not particularly high GRE Math results (around 750 I guess, still waiting for results); the exam can be retaken only in April 2015.

Therefore, the only strengths I have are high GPA and solid letters of recommendation. I guess I could send the article to Arxiv.org, but I am not sure if that is acceptable to admissions committee and I am not familiar with the process of placing the article there.

So my questions are:

Is it OK to apply this fall and in case I am not accepted to the desired program, reapply next year, in the fall of 2015?

Or there is some kind of cooldown like the one you have in industry jobs and it is wiser to skip this year's admissions and apply in 2015 with a solid application profile?
A solid GPA and letters of recommendation is nothing to sneeze at—particularly if one of the people who wrote your letter of recommendation is a co-author on the publication.

You don't need to publish the paper on arXiv if you and your co-authors don't feel it is appropriate; however, you can mention that you have a manuscript available, and submit it along with your application (if the department to which you're applying permits it!).

However, I wouldn't wait an extra year just to "improve your odds." Apply this year—if you don't like the results, try again next year.