Tenure-track application - Number of recommendation letters This question is mostly aimed at mathematicians, since I am currently in the job market for tenure-track positions in pure mathematics. 

Usually most of the job adverts say "three letters of recommendation" or "four letters of recommendation, one of which should address teaching", or variants of that. My concerns are:

1) is it ok to submit more than the number requested? Let's say they ask for 3 research letters; is it ok to submit 4? 
2) same question for teaching letters: usually only one is required for research positions. I have two available at my disposal, since I had two employers that wrote me one. Should I submit both, or just the one that I think will be more beneficial? 

Thanks!
I would not worry about submitting additional letters to places that ask for fewer.

I submitted the same number of letters of recommendation (four, I think) to all the places I applied to, regardless of how many they officially asked for.  A small number of institutions turned out to have policies that meant that they could not consider more than the number of letters that they had officially asked for in their ad.  After receiving my application, they would typically contact me and ask which letter I wanted them to throw out.  Following my discussions with the staff at a couple such institutions, I decided they were probably not places that I would want to work anyway.  They were more fixated on some administrative notion of fairness than on getting the best person for the job.  Perhaps some of those institutions just tossed my application without even contacting me; again, that doesn't sound like a place I would want to end up.

On the other hand, most institutions were happy to have additional informative letters.  Having served on hiring committees myself, I know that extra letters can provide useful additional information about a candidate, although I make a point not to be biased against applicants who submit only the minimum number of reference letters.