Combinatorial game theory is a branch of mathematics and theoretical computer science that studies games with perfect information, where two players take turns making moves and there is no element of chance. It focuses on two-player games that are typically played to a conclusion, meaning that the game ends in a win, loss, or draw. Examples of such games include chess, Go, Nim, and various other abstract and strategic games.
Algebraic combinatorics is a branch of mathematics that combines techniques from algebra, specifically linear algebra and abstract algebra, with combinatorial methods to solve problems related to discrete structures, counting, and arrangements. This area of study often involves the interplay between combinatorial objects (like graphs, permutations, and sets) and algebraic structures (like groups, rings, and fields).