Algebraic combinatorics studies the connections between combinatorics and algebraic structures. Its central topics include symmetric functions, tableaux, crystals, and so on. In this talk, I will focus on symmetric function theory and positivity problems. Then we move on to q-analogues of symmetric functions, such as the Kostka-Foulkes polynomials. Finally, I will briefly introduce Lusztig’s q-weight multiplicities, a generalization of Kostka-Foulkes polynomials, and describe a type C combinatorial formula using semistandard oscillating tableaux. This talk is based on joint work with Donghyun Kim and Seung Jin Lee.