Combinatorics is the study of combining objects by various rules to create new arrangements of objects. The objects can be anything from points and numbers to apples and oranges. Combinatorics, like algebra, numerical analysis and topology, is a important branch of mathematics. Examples of combinatorial questions are whether we can make a certain arrangement, how many arrangements can be made, and what the best arrangement for a set of objects is.

Combinatorics has grown rapidly in the last two decades making critical contributions to computer science, operations research, finite probability theory and cryptology. Computers and computer networks operate with finite data structures and algorithms which makes them perfect for enumeration and graph theory applications. Leading edge research in areas like neural networking rely on the contribution made by combinatorics.

Combinatorics can be grouped into two categories. Enumeration, which is the study of counting and arranging objects, and graph...