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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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  • 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 - GeeksforGeeks
    In Mathematics, 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, 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
  • Definition of Permutation - BYJUS
    A permutation is an arrangement of objects in a definite order The members or elements of sets are arranged here in a sequence or linear order For example, the permutation of set A= {1,6} is 2, such as {1,6}, {6,1} As you can see, there are no other ways to arrange the elements of set A
  • 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 - Meaning, Definition, Examples - Cuemath
    A permutation is an ordered arrangement of outcomes and an ordered combination For example, there are 5 chairs and 3 persons are to be seated We have 5 ways to seat the first person; 4 ways to seat the next person and 3 ways to seat the third person
  • Permutations and Combinations - GeeksforGeeks
    Permutation and Combination are the most fundamental concepts in mathematics related to picking items from a group or set Permutation is arranging items considering the order of selection from a certain group Combination is selecting items without considering order
  • 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!
  • 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
  • Permutations (Definition, types of permutations, and applications . . .
    Permutation is a mathematical technique used to count the number of possible arrangements of objects in a given order Generally, permutation is used in different fields, including computer science, statistics, combinatorics, and physics





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