I couldn't read most of the textbooks on combinatorics I've encountered. The problem is that authors usually do not explain a lot of things. For instance, they don't mention that generating function is an element of $\mathbb{C}[x]$. They never explain why identities like $\sin^2s + \cos^2 s = 1$ hold in this ring and so on. So I am looking for a book for self-study which treats this stuff rigorously and which strongly relies on abstract algebra.
Topics I want to study include generating functions and stuff one can do with them (like deriving Fibonacci sequence formula and so on), Catalan numbers and why are they interesting, $q$-binomial coefficients and a little bit about graph theory. And, of course, problems. I should also mention that I am not that interested in the subject itself but rather I often need it to deal with algebras generating by relations and that kind of stuff. And sometimes to teach contest math, too.
The main problem is that I don't know it is author not being clear enough or I am not able to understand something that simple. If author claims something which he doesn't want to prove he must explicitly say so.
My idea of good book is abstract algebra by Dummit & Foot. It explains every step or says that there is a step which we do not want to explain and it contains in the exercises with good hints provided.
\cosand\sin. For operators that don't have a command of their own, you can use\operatorname{name}. – joriki May 03 '20 at 17:54