Kombinatoriset

Kombinatoriset is a term used in some languages to denote the field of combinatorics, the mathematical study of counting, arrangement, and structure in discrete systems. It considers questions about finite sets, sequences, graphs, and other combinatorial objects, often under constraints such as limits on repetitions, orders, or adjacency.

Typical problems include counting the number of arrangements or selections, proving the existence of objects with certain properties, and classifying structures up to isomorphism. Common methods include bijective proofs, generating functions, recurrence relations, inclusion–exclusion, and the probabilistic method. Tools from algebra, geometry, and topology sometimes help solve combinatorial problems, particularly in algebraic and geometric combinatorics.

Subfields of combinatorics include graph theory, design theory, coding theory, extremal combinatorics, and matroid theory. Applications span computer science, cryptography, coding theory, network design, scheduling, and experimental design. The subject has a long history, with early problems from Euler and others, and modern development through the work of Pólya, MacMahon, and many others. Because it focuses on discrete structures, combinatorics is foundational to discrete mathematics and often intersects with optimization and algorithm design.