Short mathematics paper with a journal for 13 months

Question

I submitted a short 10 page combinatorics paper with a couple of small results, to one journal, and got a rejection in 5 weeks with the referee stating he/she has read the entire paper and that the arguments are simple.

After this, I submitted this paper to another slightly lower tier journal without mentioning this prior submission, and it has been over 13 months. I contacted the journal's editorial staff (not anyone in the editorial board; there also doesn't seem to be an option to contact the editors directly through the submission portal) after 11 months and they said new referees had been invited then.

I do not consider this paper to have significant results, but would have hoped to have heard about this by now. The journal's online portal also doesn't give an option to withdraw the paper. In this instance, is it acceptable to contact the editor by email and request a decision soon?

Edit: There is another separate short and not very significant 11 page mathematics paper where I prematurely asked the handling editor 4 months after submission, about whether the paper is with a referee and the handling editor was very kind to get back to me stating the paper was with a referee. I sent him another request after 14 months and he apologized for the delay and said they are expecting a report 'within days'. A few weeks later I got a rejection with the referee in his review of a few lines basically only commenting on the first two lines of the abstract. This particular paper was a bit poorly written, however here there was seamless communication from the handling editor I was very grateful for, but even then the process didn't feel right in the end.

In such circumstances, beyond making sure the paper is written as well as possible, what recourse does the author have when the refereeing process seems to be taking a long time?

As an aside, it is a very different culture, but I regularly referee for one of the handful of respectable expository journals in Physics and the editors start to ask for a report within a few weeks, and it is not that I don't read entire short papers carefully while still being able to submit a report in a few weeks, except a rare instance where parts of the paper look very difficult to follow or not suitable for publication in which case I make it a point to let the authors know about it as soon as possible.

Answer 1

There are parts of pure mathematics where the culture appears to be so that it is considered acceptable for a journal to sit on papers for a year or longer. (I have my own opinion on whether I think that should be acceptable, but that is not the question here.) The consequence of this is that you likely don't have much recourse: You get your review when you get it because that's just how things work. Your recourse should be that you take on a leadership position in your community (such as becoming an editor) and advocate for the change you want to see -- though that might of course be a big ask.

I will note, a propos of the question though you did not actually ask about that, that you are spending mental energy on the fate of two papers for which you readily admit that they are not strong and possibly not well written. That's putting the effort in the wrong place. Spend that energy on working on things that you know are relevant, and on producing papers you can be proud of as far as the writing itself is concerned. There is, without a doubt, a correlation between how well a paper is written from a technical perspective (regardless of the strength of the underlying material) and acceptance rates: Well written papers tend to get accepted more easily than those that are written in a way that is a nuisance to readers. Make that your mantra: Submit a paper when it is the best you can do with it, and no earlier; you will see better results.