>>11248925>Are you a computer scientist?I'm a late undergrad double majoring in math and computer science
>Does compexity theory fall under math or computer science?It's not cleanly in one or the other. It's more in the intersection, if there's to be a distinction between TCS as a subfield of math. The biggest distinction in my experience is the culture and style of the papers written.
>I'm asking as I want to study combinatoricsYou'll find both departments will probably suit your needs. I've seen many combinatorialists write algorithms papers based on their results, and I've seen combinatorial results from computer scientists make their rounds in math journals. These two camps communicate a lot with each other and the effective difference is usually their PhD title and priorities
>I don't know if computer science or math is better.At the research level, that's hard to say. Combinatorial problems in math are always present, and you'll find that mainstream computer science problems in algorithms and complexity (though that field is starting to get saturated with continuous mathematics as well) always call on discrete mathematics, especially enumerative combinatorics, generating functions, and graph theory. Really, I think it comes down to these few questions
1) which departments do you want to target for research, and which ones are easier to get in for math vs computer science?
2) what type of PhD classes do you want to take for your breadth requirements?
3) which academics do you want to follow / write with right now? You'll be able to drift from subfield to subfield as you do more work
Either way, take lots of math in the math departments, as CS departments are generally filled with people who did comprehensive math undergrads / double majors. Algorithms research is always inspired by and inspires new combinatorial and number theory results, though your main 'activity' here will be studying algorithms rather than combinatorics.
