Honestly, in this and at least one other question you are worrying about things that no one on the employer's side will care about in the least. You do not need to send a thank-you letter to any of your interviewers. If you feel like you made a personal connection with a specific faculty member, you certainly may write an email (or a letter, or whatever...) saying that you enjoyed meeting them / look forward to seeing them again / whatever. Or not: we won't care either way.
Math departments are not evaluating candidates for their general etiquette. Please remember that:
(i) We are drawing from a worldwide applicant pool, and there is no such thing as worldwide academic etiquette. We expect that once someone is hired they'll learn the local ropes.
(ii) Mathematicians have a reputation for being a bit eccentric / weird / exhibiting non-standard social behaviors. Probably this is somewhat exaggerated, but the truth is that math departments are a great haven for those whose professional competence vastly exceeds their social skills. If you are not too weird, it should not be a problem. Likability is, obviously, a positive, but we are really not running a popularity contest: the gentleman who was pretty quiet at lunch but gave a nice clear talk and has one more strong paper is going to get hired over the life of the party whose talk was a bit fuzzy and whose CV is not quite as strong.
The above is centered on research departments. Liberal arts colleges value collegiality more, but they too will make a distinction between someone who is simply socially dexterous versus someone who knows what to do in the very specific, content-related interactions they will have with students. They will not assume that because someone is well-mannered they will be good with students (or inversely): there are people whom I find painfully awkward who are wonderful with students, and students are surprisingly good at seeing the difference here as well.