# permutation

## Definitions

• WordNet 3.6
• n permutation act of changing the lineal order of objects in a group
• n permutation complete change in character or condition "the permutations...taking place in the physical world"- Henry Miller"
• n permutation the act of changing the arrangement of a given number of elements
• n permutation an event in which one thing is substituted for another "the replacement of lost blood by a transfusion of donor blood"
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Webster's Revised Unabridged Dictionary
• Permutation (Math) Any one of such possible arrangements.
• Permutation (Law) Barter; exchange.
• Permutation The act of permuting; exchange of the thing for another; mutual transference; interchange. "The violent convulsions and permutations that have been made in property."
• Permutation (Math) 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.
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Century Dictionary and Cyclopedia
• n permutation Interchange; concurrent changes; mutual change; change in general.
• n permutation Exchange; barter.
• n permutation In mathematics, a linear arrangement of objects resulting from a change of their order. Permutation differs from combination in this, that in the latter there is no reference to the order in which the quantities are combined, whereas in the former this order is considered, and consequently the number of permutations always exceeds the number of combinations.If n represents the number of quantities, then the number of permutations that can be formed out of them, taking two by two together, is n X (n-1); taken three and three together, it is n X (n-1) X (n-2); and so on. Sometimes called alternation. See combination, 5.
• n permutation In philology, the mutation or interchange of consonants, especially of allied consonants.
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Chambers's Twentieth Century Dictionary
• Permutation act of changing one thing for another:
• Permutation (math.) the arrangement of things or letters in every possible order
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## Etymology

Webster's Revised Unabridged Dictionary
L. permutatio,: cf. F. permutation,. See Permute
Chambers's Twentieth Century Dictionary
L.,—permutāreper, through, mutāre, to change.

## Usage

### In literature:

There would still remain the inverse permutation: to obtain only females and no males, or very few.
"Bramble-bees and Others" by J. Henri Fabre
Pen in hand, I arrange, permute and combine.
"The Life of the Fly" by J. Henri Fabre
There would still remain the inverse permutation: to obtain only females and no males, or very few.
"The Wonders of Instinct" by J. H. Fabre
The permutations and combinations of the stores were multiplied.
"The River War" by Winston S. Churchill
We know only five such permuted alphabets, but there may be more.
"Hebraic Literature; Translations from the Talmud, Midrashim and Kabbala" by Various
He says that every possible permutation of the four bells must be rung once, and once only.
"Amusements in Mathematics" by Henry Ernest Dudeney
And though words, too, are finite, their permutations are infinite.
"The Continental Monthly, Vol. 2, No 3, September, 1862" by Various
He is not a permutation and combination of old elements, transferred through the parents.
"Fantasia of the Unconscious" by D. H. Lawrence
Calculations of the possible combinations and permutations of a small number of objects are familiar.
"The Classification of Patents" by United States Patent Office
What could he imagine, except combinations and permutations of his own memories?
"Suite Mentale" by Gordon Randall Garrett
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### In poetry:

French Deck. Solitary stroker of cards. He
dealt himself a hand. Turn stills of the past in
unending permutations, shuffle and begin. Sort
the images again. And sort them again. This
game reveals germs of truth, and death.
"Notes On Vision" by James Douglas Morrison

### In news:

As we talked about on Friday, the Knicks have gone through so many different permutations in this season alone that it's enough to give fans whiplash, or vertigo, or some combination of both.
One of the ISAM Live 2.0 set's many stunning permutations.
Cycles, and the cycle decomposition of a permutation.
The word and its permutations come up a lot when the singer-keyboardist-producer talks about Johnny Headband 's Who Cooks for You.
Permut Presentations presentation of a James W Evangelatos, Julie Lott Gallo production.
Produced by David Permut, Mark Sennet, Julie Lott Gallo, James W Evangelatos.
There is a brief but thorough description of what a combinatorial object is, such as permutations and subsets.
Combinations and permutations are fairly rare on the SAT.
Questions that involve arranging a group are " permutations ," since in an arrangement the order of things is important.
Now that we have the permutation fully specified, we'll use it to learn a little about how the CTC permutation works — in particular, we're going to learn about cycles in permutations and try to understand the cycle structure of a CTC.
Randomization was based on permuted blocks, with a block size of 4.
John Whitney's Permutations by Klax.
One of the first theorems on permutation routing, proved by V.E.
Columnar transposition ciphers and permutations, oh my.
Run a few permutations, described below, and Xenopohon ends up using the word "paradeisos," which he used to refer to the walled gardens of Persia.
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### In science:

According to Section 10.2, B -permutations for the associahedron are 312-avoiding permutations and h-polynomial is equal to the sum hPB(Pathn ) (t) = Pw qpeak(w)−1 over all 312-avoiding permutations w ∈ Sn .
Faces of Generalized Permutohedra
Our goal here is therefore to present a simple bijection between permutations and permutation tableaux that maps the descents of the permutation to the columns of the tableau.
A simple bijection between permutation tableaux and permutations
Williams, Permutation tableaux and permutation patterns, to appear in the Journal of Combinatorial Theory, Series A. arXiv:math.
A simple bijection between permutation tableaux and permutations
We determine exactly the probability of ﬁnding the tra jectory of such a permutation-generated random walk at site X at time n, obtain the probability measure of different excursions and deﬁne the asymptotic distribution of the number of ”U-turns” of the tra jectories - permutation ”peaks” and ”through”.
Random patterns generated by random permutations of natural numbers
First we draw uniformly a permutation and after that we pick N initial points which are permuted according to the chosen permutation to obtain N terminal points.
Asymptotic Feynman-Kac formulae for large symmetrised systems of random walks
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