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permutation    音标拼音: [p,ɚmjut'eʃən]
n. 交换,排列

交换,排列

permutation
排列;置换

permutation
排列 置换

permutation
n 1: an event in which one thing is substituted for another;
"the replacement of lost blood by a transfusion of donor
blood" [synonym: {substitution}, {permutation},
{transposition}, {replacement}, {switch}]
2: the act of changing the arrangement of a given number of
elements
3: complete change in character or condition; "the
permutations...taking place in the physical world"- Henry
Miller
4: act of changing the lineal order of objects in a group

Permutation \Per`mu*ta"tion\ (p[~e]r`m[-u]"t[=a]"sn[u^]n), n.
[L. permutatio: cf. F. permutation. See {Permute}.]
1. The act of permuting; exchange of the thing for another;
mutual transference; interchange.
[1913 Webster]

The violent convulsions and permutations that have
been made in property. --Burke.
[1913 Webster]

2. (Math.)
(a) 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.
(b) Any one of such possible arrangements.
[1913 Webster]

3. (Law) Barter; exchange.
[1913 Webster]

{Permutation lock}, a lock in which the parts can be
transposed or shifted, so as to require different
arrangements of the tumblers on different occasions of
unlocking.
[1913 Webster]

60 Moby Thesaurus words for "permutation":
alteration, alternation, avatar, battledore and shuttlecock,
catabolism, catalysis, commutation, consubstantiation, cooperation,
counterchange, cross fire, displacement, exchange, give-and-take,
heterotopia, innovation, interchange, intermutation, interplay,
lex talionis, measure for measure, metabolism, metagenesis,
metamorphism, metamorphosis, metastasis, metathesis,
metempsychosis, modification, mutant, mutated form, mutation,
mutual admiration, mutual support, mutual transfer, mutuality,
novelty, quid pro quo, reciprocality, reciprocation, reciprocity,
reincarnation, retaliation, something for something, sport,
tit for tat, transanimation, transfiguration, transfigurement,
transformation, transformism, translation, translocation,
transmigration, transmogrification, transmutation, transposal,
transposition, transubstantiation, vicissitude

1. An ordering of a certain number of elements
of a given set.

For instance, the permutations of (1,2,3) are (1,2,3) (2,3,1)
(3,1,2) (3,2,1) (1,3,2) (2,1,3).

Permutations form one of the canonical examples of a "{group}"
- they can be composed and you can find an inverse permutation
that reverses the action of any given permutation.

The number of permutations of r things taken from a set of n
is

n P r = n! / (n-r)!

where "n P r" is usually written with n and r as subscripts
and n! is the {factorial} of n.

What the football pools call a "permutation" is not a
permutation but a {combination} - the order does not matter.

2. A {bijection} for which the {domain} and {range} are the
same set and so

f(f'(x)) = f'(f(x)) = x.

(2001-05-10)

PERMUTATION, civil law. Exchange; barter.
2. This contract is formed by the consent of the parties, but delivery
is indispensable; for, without it, it mere agreement. Dig. 31, 77, 4; Code,
4, 64, 3.
3. Permutation differs from sale in this, that in the former a delivery
of the articles sold must be made, while in the latter it is unnecessary. It
agrees with the contract of sale, however, in the following particulars: 1.
That he to whom the delivery is made acquires the right or faculty of
prescribing. Dig. 41, 3, 4, 17. 2. That the contracting parties are bound to
guaranty to each other the title of the things delivered. Code, 4, 64, 1. 3.
That they are bound to take back the things delivered, when they have latent
defects which they have concealed. Dig. 21, 1, 63. See Aso & Man. Inst. B.
2, t. 16, c. 1; Nutation; Transfer.


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  • 排列 - 维基百科，自由的百科全书
    排列 P (3,3)=6 排列 （英語： Permutation）或 置換 是將相異物件或符號根據確定的順序重排。 每個順序都稱作一個 排列[注 1]。 例如，從一到六的 數字 有720種排列，對應於由這些數字組成的所有不重複亦不闕漏的序列，例如"4, 5, 6, 1, 2, 3" 與 1, 3, 5, 2, 4, 6。
  • Combinations and Permutations - Math is Fun
    There are basically two types of permutation: Repetition is Allowed: such as the lock above It could be "333" No Repetition: for example the first three people in a running race You can't be first and second 1 Permutations with Repetition These are the easiest to calculate When a thing has n different types we have n choices each time!
  • PERMUTATION中文 (简体)翻译：剑桥词典 - Cambridge Dictionary
    PERMUTATION翻译：（数学的）排列，置换, （几种中的）一种。 了解更多。
  • 排列（组合数学术语）_百度百科
    重复排列 (permutation with repetition [2])是一种特殊的排列。 从n个不同元素中可重复地选取m个元素。 按照一定的顺序排成一列，称作从n个元素中取m个元素的可重复排列。 当且仅当所取的元素相同，且元素的排列顺序也相同，则两个排列相同。
  • 置换和排列 - OI Wiki
    一个集合 到自身的双射（即一一对应） 称为 的一个 置换 （permutation）。 如果集合 上还具有 全序 关系，则它的一个置换也常称作一个 （全）排列。
  • Permutation - Math. net
    A permutation refers to a selection of objects from a set of objects in which order matters A phone number is an example of a ten number permutation; it is drawn from the set of the integers 0-9, and the order in which they are arranged in matters
  • Permutations and combinations | Description, Examples, Formula . . .
    permutations and combinations, the various ways in which objects from a set may be selected, generally without replacement, to form subsets This selection of subsets is called a permutation when the order of selection is a factor, a combination when order is not a factor
  • Permutations | Brilliant Math Science Wiki
    In combinatorics, a permutation is an ordering of a list of objects For example, arranging four people in a line is equivalent to finding permutations of four objects More abstractly, each of the following is a permutation of the letters
  • Permutation -- from Wolfram MathWorld
    A permutation, also called an "arrangement number" or "order," is a rearrangement of the elements of an ordered list S into a one-to-one correspondence with S itself The number of permutations on a set of n elements is given by n! (n factorial; Uspensky 1937, p 18)





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