permutation
C1Formal, Technical
Definition
Meaning
A specific arrangement or ordering of a set of items.
In mathematics, a permutation is an ordered arrangement of all or part of a set of objects. In general use, it can refer to any variation or change in order, sequence, or combination.
Linguistics
Semantic Notes
Implies a deliberate or systematic ordering. Distinct from 'combination' in mathematics, where order does not matter.
Dialectal Variation
British vs American Usage
Differences
No significant difference in core meaning. Slightly higher frequency in technical contexts (e.g., mathematics, computing, statistics) in both varieties.
Connotations
Neutral to formal. Connotes precision, mathematics, and systematic change.
Frequency
Low frequency in everyday conversation; common in academic, scientific, and some business contexts (e.g., logistics, scheduling).
Vocabulary
Collocations
Grammar
Valency Patterns
[permutation] of [something]consider/explore/test [the permutations]Vocabulary
Synonyms
Strong
Neutral
Weak
Vocabulary
Antonyms
Usage
Context Usage
Business
Used in strategic planning or scenario analysis: 'We modeled every permutation of market conditions.'
Academic
Core term in mathematics, statistics, and computer science: 'The algorithm generates all permutations of the data set.'
Everyday
Rare in casual speech. Might be used humorously or emphatically: 'I've tried every permutation of tying this scarf!'
Technical
Precise term in combinatorics, cryptography, and algorithm design.
Examples
By Part of Speech
noun
British English
- The safe's code is one permutation of these six numbers.
- We need to consider each permutation of team roles carefully.
American English
- The software tests every possible password permutation.
- A new permutation of the trade deal was proposed.
Examples
By CEFR Level
- The coach tried a different permutation of players for the second half.
- The study examined various permutations of the experimental variables to find the optimal setup.
- Cryptographic security often relies on the vast number of permutations available for a given key space, making brute-force attacks computationally infeasible.
Learning
Memory Aids
Mnemonic
Think of PERM in 'permanent' – a permutation is a permanent (or fixed) ARRANGEMENT of items in a specific order.
Conceptual Metaphor
LIFE AS A DECK OF CARDS: 'Exploring the permutations of one's career' suggests trying out different ordered sequences of life events.
Watch out
Common Pitfalls
Translation Traps (for Russian speakers)
- Not synonymous with перестановка (perestanovka) in all contexts, which is more general. The mathematical term перестановка is a direct equivalent.
Common Mistakes
- Confusing 'permutation' (order matters) with 'combination' (order doesn't matter). Using it as a fancy synonym for 'change' without the concept of ordered arrangement.
Practice
Quiz
Which of the following best describes a 'permutation'?
FAQ
Frequently Asked Questions
In permutations, the order of items matters (e.g., PIN code 1234 is different from 4321). In combinations, the order does not matter (e.g., a fruit salad with apples and bananas is the same combination as one with bananas and apples).
No, it is primarily used in formal, academic, scientific, and technical contexts. In everyday speech, words like 'arrangement', 'order', or 'variation' are more common.
No, the related verb is 'permute'. 'Permutation' is strictly a noun.
For selecting and arranging 'r' items from a set of 'n' distinct items, the number of permutations is n! / (n-r)! (where '!' denotes factorial).