Combinatorial problems of other types had been considered since antiquity.

Combinatorial search algorithms are typically concerned with problems that are NP-hard.

* Combinatorial optimization problems such as parsing and the knapsack problem.

Multiobjective Combinatorial Optimization ( MOCO ) constitutes a special category of such problems posing substantial computational difficulty ( see Ehrgott and Gandibleux, 2002, for a review ).

:: Research areas: Models of Computation and Complexity ( automata and formal language theory and applications, Natural computing, bioinformatics, riceInformatics, formal models for e-voting ), Algorithmics, Designs and Implementations ( visualization and implementations, algorithmics for hard problems, algorithmic game theory, scheduling problem ), Combinatorial Networks, Information Technology in Education.

In his 1972 paper, " Reducibility Among Combinatorial Problems ", Richard Karp used Stephen Cook's 1971 theorem that the boolean satisfiability problem is NP-complete ( also called the Cook-Levin theorem ) to show that there is a polynomial time many-one reduction from the boolean satisfiability problem to each of 21 combinatorial and graph theoretical computational problems, thereby showing that they are all NP-complete.

Combinatorial Game Theory, a branch of applied mathematics, is a topic relevant to computer Go.

Combinatorial game theory ( CGT ) is a branch of applied mathematics and theoretical computer science that studies sequential games with perfect information, that is, two-player games which have a position in which the players take turns changing in defined ways or moves to achieve a defined winning condition.

Combinatorial design theory is the part of combinatorial mathematics that deals with the existence, construction and properties of systems of finite sets whose arrangements satisfy generalized concepts of balance and / or symmetry.

* Combinatorial commutative algebra

Category: Combinatorial game theory

* Mathematics: Approximation theory — Arakelov theory — Asymptotic theory — Bifurcation theory — Catastrophe theory — Category theory — Chaos theory — Choquet theory — Coding theory — Combinatorial game theory — Computability theory — Computational complexity theory — Deformation theory — Dimension theory — Ergodic theory — Field theory — Galois theory — Game theory — Graph theory — Group theory — Hodge theory — Homology theory — Homotopy theory — Ideal theory — Intersection theory — Invariant theory — Iwasawa theory — K-theory — KK-theory — Knot theory — L-theory — Lie theory — Littlewood – Paley theory — Matrix theory — Measure theory — Model theory — Morse theory — Nevanlinna theory — Number theory — Obstruction theory — Operator theory — PCF theory — Perturbation theory — Potential theory — Probability theory — Ramsey theory — Rational choice theory — Representation theory — Ring theory — Set theory — Shape theory — Small cancellation theory — Spectral theory — Stability theory — Stable theory — Sturm – Liouville theory — Twistor theory

:: Note: The physical fully connected mesh topology is generally too costly and complex for practical networks, although the topology is used when there are only a small number of nodes to be interconnected ( see Combinatorial explosion ).

* Combinatorial topology –

It should not be confused with Discrete geometry ( Combinatorial geometry ).

* Combinatorial computational geometry, also called algorithmic geometry, which deals with geometric objects as discrete entities.

* Combinatorial geometry –

See also: Category: Combinatorial group theory.

These ideas were well worked up in his 1949 paper ` Combinatorial homotopy II ', which also introduced the important idea of a free crossed module.

Combinatorial games are generally, by convention, put into a form where one player wins when the other has no moves remaining.

Combinatorial game theory has several ways of measuring game complexity.

Category: Combinatorial optimization

* Combinatorial optimization

* Combinatorial optimization

Category: Combinatorial optimization

Category: Combinatorial optimization

* Combinatorial optimization

* Combinatorial optimization –

Category: Combinatorial optimization

* Combinatorial optimization

Category: Combinatorial optimization

Category: Combinatorial optimization

Category: Combinatorial optimization

Category: Combinatorial optimization

Category: Combinatorial optimization

Combinatorial analysis and / or computer simulation is necessary to complete the task.

Combinatorial chemistry involves the rapid synthesis or the computer simulation of a large number of different but often structurally related molecules or materials.

Combinatorial processes generate very large numbers in statistical mechanics.

* Combinatorial pattern matching, a research area and a conference on combinatorial algorithms for strings, sequences, and trees.

# Volume 4A: Combinatorial Algorithms, Part 1, 2011.

# Volume 4, Fascicle 0: Introduction to Combinatorial Algorithms and Boolean Functions.

# Volume 4, Fascicle 4: Generating All Trees — History of Combinatorial Generation, 2006.

Combinatorial mutagenesis is a technique whereby large number of mutants may be screened for a particular characteristic.

Combinatorial test design enables users to get greater test coverage with fewer tests.

" In Algorithms and Classification in Combinatorial Group Theory, pages 1 – 60.

Combinatorial chemistry is especially common in CADD ( Computer aided drug design ) and can be done online with web based software, such as Molinspiration.

Combinatorial Problems, Discrete Optimization 3 ( 2006 ), 288-298.

* Combinatorial auction is any auction for the simultaneous sale of more than one item where bidders can place bids on an " all-or-nothing " basis on " packages " rather than just individual items.

A web-based server implementing the method and providing a database of pairwise alignments of structures in the Protein Data Bank is located at the Combinatorial Extension website.

( i ) Combinatorial completeness.

Combinatorial processes rapidly generate even larger numbers.

* Information on Primitive and Irreducible Polynomials, The ( Combinatorial ) Object Server.

* Ralph P. Grimaldi, Discrete and Combinatorial Mathematics, ISBN 0-201-19912-2.

Combinatorial search algorithms achieve this efficiency by reducing the effective size of the search space or employing heuristics.

Combinatorial search algorithms are normally implemented in an efficient imperative programming language, in an expressive declarative programming language such as Prolog, or some compromise, perhaps a functional programming language such as Haskell, or a multi-paradigm language such as LISP.