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.

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