Combinatorics

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A branch of mathematics focusing on the study of finite or countable discrete structures. At its core, combinatorics involves selecting, arranging, constructing, classifying, and counting or listing things, often to determine the number of possible configurations that meet specific criteria.

Objects within a set. Finite sets of discrete elements (as opposed to continuous systems, or gradual change).

This can range from simple problems, such as counting the number of ways to arrange a set of books on a shelf, to more complex issues involving the structure of networks or optimising routes within a system. Fundamental principles of combinatorics include permutations, where the order of arrangement matters, and combinations, where the order does not matter.

Existence problem: Does ⬚⬚⬚ exist?
Construction problem: If ⬚⬚⬚ exists, how can we construct it?
Enumeration problem: How many ⬚⬚⬚ are there?
Optimisation problem: Which ⬚⬚⬚ is best?

Ordered selections with repetition? Ordered selections without repetition (permutations)? Underordered selections without repetition (combinations)? Unordereded selections with repetition (distributions)?

• [?] What are the limitations of combinatorial methods for solving real-world problems?
• [&] See also: combinatorial models of innovation?
• [&] See also: combinatorics in divination?

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