combinatorics

Statistics

(noun)

A branch of mathematics that studies (usually finite) collections of objects that satisfy specified criteria.

Related Terms

  • polynomial
Calculus

(noun)

a branch of mathematics that studies (usually finite) collections of objects that satisfy specified criteria and their structures

Related Terms

  • Z-transform

Examples of combinatorics in the following topics:

  • Counting Rules and Techniques

    • Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures.
    • Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures.
    • Combinatorial techniques are applicable to many areas of mathematics, and a knowledge of combinatorics is necessary to build a solid command of statistics.
    • Aspects of combinatorics include: counting the structures of a given kind and size, deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria.
  • Total Number of Subsets

    • These numbers also arise in combinatorics, where $n^b$ gives the number of different combinations of $b$ elements that can be chosen from an $n$-element set.
  • Power Series

    • These power series arise primarily in real and complex analysis, but also occur in combinatorics (under the name of generating functions) and in electrical engineering (under the name of the $Z$-transform).
  • Theoretical Probability

    • Calculating the number of ways that certain patterns can be formed is part of the field of combinatorics.
  • Proof by Mathematical Induction

    • The choice between $n=0$ and $n=1$ in the base case is specific to the context of the proof: If 0 is considered a natural number, as is common in the fields of combinatorics and mathematical logic, then $n=0$.
  • Permutations

    • The study of permutations generally belongs to the field of combinatorics.
  • Binomial Expansions and Pascal's Triangle

    • The binomial coefficient also arises in combinatorics, where it gives the number of different combinations of $b$ elements that can be chosen from a set of $n$ elements.
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