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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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  • Permutation - Wikipedia
    Permutation According to the first meaning of permutation, each of the six rows is a different permutation of three distinct balls In mathematics, a permutation of a set can mean one of two different things: an arrangement of its members in a sequence or linear order, or the act or process of changing the linear order of an ordered set [1]
  • Combinations and Permutations - Math is Fun
    In English we use the word combination loosely, without thinking if the order of things is important In other words:
  • 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
  • Permutation - GeeksforGeeks
    Permutation 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 Note: In Permutations, order matters; for example, (2, 1) and (1, 2) are counted as different
  • Permutations Calculator nPr
    Find the number of ways of getting an ordered subset of r elements from a set of n elements as nPr (or nPk) Permutations calculator and permutations formula Free online permutations calculator
  • Permutations - Meaning, Definition, Examples - Cuemath
    Permutations Permutations are different ways of arranging objects in a definite order It can also be expressed as the rearrangement of items in a linear order of an already ordered set The symbol \ (^n {P_r}\) is used to denote the number of permutations of n distinct objects, taken r at a time It locks schedules of buses, trains or flights, allocation of zip codes and phone numbers These
  • Permutation - Math. net
    Permutation 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
  • Counting, permutations, and combinations | Khan Academy
    How many outfits can you make from the shirts, pants, and socks in your closet? Address this question and more as you explore methods for counting how many possible outcomes there are in various situations Learn about factorial, permutations, and combinations, and look at how to use these ideas to find probabilities
  • Permutation -- from Wolfram MathWorld
    A permutation, also called an "arrangement number" or "order," is a rearrangement of the elements of an ordered list into a one-to-one correspondence with itself The number of permutations on a set of elements is given by ( factorial; Uspensky 1937, p 18) For example, there are permutations of , namely and , and permutations of , namely , , , , , and The permutations of a list can be
  • 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





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