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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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