permutation

/,pə:mju:'teiʃn/
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permutation

A student writes down all possible permutations of the letters A, B, and C.

Definition
  1. Noun:
    • An act of changing the linear order of objects in a group: A permutation is the rearrangement of the order of a set of items.
    • A complete change in character or condition: Permutation can also refer to a fundamental or thorough transformation.
    • (Mathematics) The act of changing the arrangement of a given number of elements: In mathematics, a permutation is a specific arrangement of all or part of a set of objects, with regard to the order of the arrangement.
Usage Examples
  • Noun:
    • The teacher asked us to list all possible permutations of the letters A, B, and C.
    • The constant permutations in company policy are confusing for the staff.
    • In this puzzle, you must find the correct permutation of the numbers to open the lock.
Advanced Usage

  • "Permutation and combination": A fundamental concept in combinatorics, a branch of mathematics dealing with counting, arrangement, and probability.

    • The chapter on permutation and combination is crucial for understanding probability theory.

  • "Every permutation imaginable": Used to emphasize that all possible variations or arrangements have been considered.

    • We have tested every permutation imaginable to solve this software bug.
Variants and Related Words

  • Permute (verb): To change the order or arrangement of.

    • The algorithm is designed to permute the sequence randomly.

  • Permutational (adjective): Relating to or involving permutation.

    • The study focused on the permutational complexity of the system.
Synonyms
  • Rearrangement: The action or process of changing the position or order of something.
  • Transformation: A thorough or dramatic change in form or appearance.
  • Variation: A change or slight difference in condition, amount, or level.
Related Phrases

  • Cyclic permutation: (Mathematics) A permutation that shifts all elements of a set by a fixed offset, placing the last element first.

    • A cyclic permutation of (1,2,3) is (2,3,1).

  • Even/Odd permutation: (Mathematics) A classification based on the number of pairwise swaps (transpositions) needed to achieve the arrangement from the original order.

    • Determining if a permutation is even or odd is important in calculating determinants.
permutation

A student writes down all possible permutations of the letters A, B, and C.

Noun
  1. act of changing the lineal order of objects in a group
  2. complete change in character or condition
    • the permutations...taking place in the physical world- Henry Miller
  3. the act of changing the arrangement of a given number of elements
  4. an event in which one thing is substituted for another
    • the replacement of lost blood by a transfusion of donor blood

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