What is Combinatorics? Combinatorics is a young field of mathematics, starting to be an independent branch only in the 20th century. However, combinatorial methods and problems have been around ever since. Many combinatorial problems look entertaining and one can easily say that roots of combinatorics lie in mathematical creativity and games.
Nonetheless, this field has grown to be of great importance in today’s world, not only because of its use for other fields like physical sciences, social sciences, biological sciences, information theory and computer science. Combinatorics is concerned with: Arrangements of elements in a set into patterns satisfying specific rules, generally referred to as discrete structures. Here “discrete” (as opposed to continuous) typically also means finite, although we will consider some infinite structures as well. •The existence, enumeration, analysis and optimization of discrete structures.
Interconnections, generalizations- and specialization-relations between several discrete structures. Existence: We want to arrange elements in...