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permutation    音標拼音: [p,ɚmjut'eʃən]
n. 交換,排列

交換,排列

permutation
排列;置換

permutation
排列 置換

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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英文字典中文字典相關資料:
  • Permutation - Wikipedia
    Permutations are used in almost every branch of mathematics and in many other fields of science In computer science, they are used for analyzing sorting algorithms; in quantum physics, for describing states of particles; and in biology, for describing RNA sequences
  • Combinations and Permutations - Math is Fun
    When the order doesn't matter, it is a Combination When the order does matter it is a Permutation So, we should really call this a "Permutation Lock"! In other words: A Permutation is an ordered Combination To help you to remember, think " P ermutation P osition" There are basically two types of permutation:
  • Permutations Calculator nPr
    There are n! ways of arranging n distinct objects into an ordered sequence, permutations where n = r The number of ways to choose a sample of r elements from a set of n distinct objects where order does not matter and replacements are not allowed
  • Permutation - GeeksforGeeks
    In Mathematics, a Permutation is defined as a mathematical concept that determines the number of possible arrangements for a specific set of elements Therefore, it plays a big role in computer science, cryptography, and operations research
  • Permutations and combinations | Description, Examples . . .
    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 - Meaning, Definition, Examples - Cuemath
    Permutation means "both selection and arrangement" whereas combination means just the "selection" Wherever the ordering of objects does not matter, we use combinations there
  • Permutations P (n,r) (video lessons, examples, solutions)
    What Is Permutation? A permutation is an arrangement, or listing, of objects in which the order is important In previous lessons, we looked at examples of the number of permutations of n things taken n at a time Permutation is used when we are counting without replacement and the order matters





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