# Definitions for **permutation**ˌpɜr myʊˈteɪ ʃən

### This page provides all possible meanings and translations of the word **permutation**

### Random House Webster's College Dictionary

per•mu•ta•tionˌpɜr myʊˈteɪ ʃən(n.)

the act of permuting or permutating; alteration; transformation.

Math. the act of changing the order of set elements arranged in a particular way, as abc into acb or any of the resulting arrangements.

bac.

**Category:**Math**Ref:**Compare combination (def. 8). 8

#### Origin of **permutation**:

1325–75; ME permutacioun (< AF, MF) < L permūtātiō= permūtā(re) to permute+ -tiō -tion

per`mu•ta′tion•ist(n.)

### Princeton's WordNet

substitution, permutation, transposition, replacement, switch(noun)

an event in which one thing is substituted for another

"the replacement of lost blood by a transfusion of donor blood"

permutation(noun)

the act of changing the arrangement of a given number of elements

permutation(noun)

complete change in character or condition

"the permutations...taking place in the physical world"- Henry Miller

permutation(noun)

act of changing the lineal order of objects in a group

### Wiktionary

permutation(Noun)

A one-to-one mapping from a finite set to itself.

This permutation takes each element to the one following it, with the last mapped back to the first.

permutation(Noun)

An ordering of a finite set of distinct elements.

There are six permutations of three elements, e.g. {abc, acb, bac, bca, cab, cba}.

permutation(Noun)

A transformation of a set's prime form, by applying one or more of certain operations, specifically, transposition, inversion, and retrograde.

**Origin:** From permutacion (French: permutation).

### Webster Dictionary

Permutation(noun)

the act of permuting; exchange of the thing for another; mutual transference; interchange

Permutation(noun)

the arrangement of any determinate number of things, as units, objects, letters, etc., in all possible orders, one after the other; -- called also alternation. Cf. Combination, n., 4

Permutation(noun)

any one of such possible arrangements

Permutation(noun)

barter; exchange

### Freebase

Permutation

In mathematics, the notion of permutation is used with several slightly different meanings, all related to the act of permuting objects or values. Informally, a permutation of a set of objects is an arrangement of those objects into a particular order. For example, there are six permutations of the set {1,2,3}, namely, and. For example, an anagram of a word is a permutation of its letters. The study of permutations in this sense generally belongs to the field of combinatorics. The number of permutations of n distinct objects is n×××⋯×2×1, which is commonly denoted as "n factorial" and written "n!". Permutations occur, in more or less prominent ways, in almost every domain of mathematics. They often arise when different orderings on certain finite sets are considered, possibly only because one wants to ignore such orderings and needs to know how many configurations are thus identified. For similar reasons permutations arise in the study of sorting algorithms in computer science. In algebra and particularly in group theory, a permutation of a set S is defined as a bijection from S to itself. This is related to the rearrangement of S in which each element s takes the place of the corresponding f. The collection of such permutations form a symmetric group. The key to its structure is the possibility to compose permutations: performing two given rearrangements in succession defines a third rearrangement, the composition. Permutations may act on composite objects by rearranging their components, or by certain replacements of symbols.

# Translations for **permutation**

### Kernerman English Multilingual Dictionary

permutation(noun)

a particular order in which things are arranged

We can write down these numbers in various permutations.

- volgordeAfrikaans
- إبْدال، تَبْديلArabic
- пермутацияBulgarian
- permutaçãoPortuguese (BR)
- obměnaCzech
- die UmstellungGerman
- kombinationsmulighedDanish
- συνδυασμός, παραλλαγήGreek
- permutaciónSpanish
- permutatsioonEstonian
- جایگشتFarsi
- permutaatioFinnish
- arrangementFrench
- תְמוּרָהHebrew
- क्रमचयHindi
- izmjena, promjena poretkaCroatian
- permutációHungarian
- urutanIndonesian
- umröðun, umbreytingIcelandic
- combinazione, sistemaItalian
- 順列Japanese
- 치환, 순열Korean
- sukeitimas, derinys, kombinacijaLithuanian
- permutācija; kombinācijaLatvian
- pilih aturMalay
- combinatieDutch
- rekkefølge, permutasjonNorwegian
- kombinacja, połączeniePolish
- جایگشتPersian
- بشپړ بدلون ، تغير، اوښتونPashto
- permutaçãoPortuguese
- permutareRomanian
- расположениеRussian
- permutáciaSlovak
- razporeditevSlovenian
- permutacijaSerbian
- permutationSwedish
- การสลับลำดับThai
- permitasyon, devşirimTurkish
- 排列Chinese (Trad.)
- перестановкаUkrainian
- ترتيبUrdu
- sự đổi trật tựVietnamese
- 排列Chinese (Simp.)

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"permutation." *Definitions.net.* STANDS4 LLC, 2014. Web. 25 Apr. 2014. <http://www.definitions.net/definition/permutation>.