Combinatorics is a sub-discipline of Algebra which is concerned with the study of combination, enumeration and permutation of sets of elements. One of the main aspects of combinatorics is the study of combinatorial structures found in an algebraic context. It draws on principles from Group Theory and Representation Theory.
Representation Theory is the study of abstract algebraic structures. It aims to represent their elements in the form of linear transformations of vector spaces; in essence, representation makes an abstract mathematical concept more concrete. Thus, it can be seen that this particular theory is especially prominent in the study of Combinatorics – as it hints at the appearance of enumerative methods in the area of algebraic geometry.
Algebraic Combinatorial problems are not limited to the discipline of algebra, but rather they can extend into the realm of probability, geometry and topology. In fact, this study can go even further, as it has many applications in the fields of optimization, computer science and physics. Thus, understanding Combinatorics is crucial for the study of Algebra as well as other disciplines which examines combination, enumeration and permutation.