# Definition of combinatorics in US English:

## combinatorics

### plural noun

• treated as singular The branch of mathematics dealing with combinations of objects belonging to a finite set in accordance with certain constraints, such as those of graph theory.

• ‘The problems which attracted him most were problems in combinatorics, graph theory, and number theory.’
• ‘It has proved to be the computational method of choice for symbolic manipulation in algebraic geometry, differential equations, and combinatorics.’
• ‘His thesis work combined algebra and combinatorics into the new field of matrix theory.’
• ‘Is any computing unrelated to quantum computing now a pointless exercise in combinatorics?’
• ‘The reason is a topic for another note, on the limitations of combinatorics in geometry.’
• ‘His basic research contributions span complex analysis, mathematical physics, probability theory, geometry, and combinatorics.’
• ‘This triangle has an elementary use in probability and combinatorics, and both the series of triangular numbers and the Fibonacci series can be derived from it.’
• ‘It is important in the modern theory of combinatorics.’
• ‘It is a lot easier to evaluate the quality of a theoretical edifice, and in fact one of the knocks on combinatorics is precisely the ‘apparent’ lack of such an edifice.’
• ‘Generating functions have numerous applications in mathematics, especially in combinatorics, probability theory, statistics, the theory of Markov chains, and number theory.’
• ‘His major mathematical contributions are to finite field theory, number theory, and combinatorics.’
• ‘His early works range over number theory, statistics, combinatorics, game theory, as well as his principal interest of commutative algebra.’
• ‘They worked on topics such as soluble groups, combinatorics, and matrix theory.’
• ‘He produced his own versions of logarithms, infinite series, and combinatorics which did not follow the style of western mathematics but his research naturally developed out of the foundations of Chinese mathematics.’
• ‘Often in combinatorics when an identity establishes the equality to two sets defined in different ways, one desires a bijection, namely, a one-to-one correspondence that converts members of one set to the other in a natural fashion.’
• ‘In particular he made contributions of major importance in the theory of polytopes, non-euclidean geometry, group theory and combinatorics.’
• ‘His interests were mainly in number theory and combinatorics, though they ranged into topology and other areas of mathematics.’
• ‘Cryptography has generated number theory, algebraic geometry over finite fields, algebra, combinatorics and computers.’
• ‘My research is in combinatorics and number theory.’
• ‘His work led to considerable activity in the new area of algebraic combinatorics.’

### Origin

1940s: from combinatorial (see combination), influenced by German Kombinatorik.

## combinatorics

/ˌkämbənəˈtôriks//ˌkɑmbənəˈtɔrɪks/