# permutable

## Definitions

• WordNet 3.6
• adj permutable capable of changing sequence
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Webster's Revised Unabridged Dictionary
• a Permutable Capable of being permuted; exchangeable.
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Century Dictionary and Cyclopedia
• permutable Capable of being permuted; exchangeable; interchangeable.
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Chambers's Twentieth Century Dictionary
• adj Permutable per-mū′ta-bl that may be changed one for another
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## Etymology

Webster's Revised Unabridged Dictionary
Cf. F. permutable,
Chambers's Twentieth Century Dictionary
L.,—permutāreper, through, mutāre, to change.

## Usage

### In literature:

SOCRATES: That may be variously interpreted; and yet more variously if a little permutation is allowed.
"Cratylus" by Plato
A was undermining B, D was undermining C, and so on in all possible combinations and permutations.
"War and Peace" by Leo Tolstoy
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
In abortion it exists, but in a stunted and dwarfed, but not otherwise permuted state.
"Vegetable Teratology" by Maxwell T. Masters
They were mere permutations of known quantities.
"The Rainbow" by D. H. (David Herbert) Lawrence
Watch now the permutations and combinations the author develops from this general situation.
"Dramatic Technique" by George Pierce Baker
Those ten little Arabic symbols and their combinations and permutations held a fascination for him.
"The Sin of Monsieur Pettipon" by Richard Connell
We can do this in twenty-four different ways by forming all permutations of the letters.
"Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6" by Various
Then began fresh combinations and permutations of the talk.
"A Crooked Mile" by Oliver Onions
Any two translations are permutable with each other, and give when combined another translation.
"Encyclopaedia Britannica, 11th Edition, Volume 12, Slice 6" by Various
In genuine Lancashire we have first the old-accustomed permutations of the vowels.
"Lancashire" by Leo H. (Leo Hartley) Grindon
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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:

Proof All claims follow from the analogous properties of the measure µ∞, which is invariant under the shift and permutations of coordinates, and from the fact that the mapping FT commutes with the action of the shift and permutations.
Random Metric Spaces and Universality
To prove our lower bound, we exhibit an explicit complex-valued test function which typically takes very different values for permutations arising from the cyclic-to-random-shufﬂ e and for uniform random permutations; we expect that this test function may be useful in future analysis of RC4.
Shuffling by semi-random transpositions
This leading order is described by summing over non-crossing permutations, but in contrast to the semi-circular case, all permutations contribute, not just pairings.
Second Order Freeness and Fluctuations of Random Matrices: I. Gaussian and Wishart matrices and Cyclic Fock spaces
We use the term fragmented permutation of [n] for a pair γ = (σ, λ) ∈ S Sn × Cn, where S Sn is the set of all permutations of [n], and Cn is the set of all compositions of n.
Regenerative partition structures
Deﬁnition 8 The q(n, ·)-chain on permutations of [n] is the q(n, ·)-chain on fragmented permutations of [n] pushed forward by pro jection from (σ, λ) to σ .
Regenerative partition structures
As a consequence, it is easily obtained that a GUE matrix with randomly permuted rows has asymptotically a circular ∗–distribution, and that a Wishart matrix with randomly permuted rows is asymptotically R-diagonal.
Asymptotic Freeness of Random Permutation Matrices from Gaussian Matrices
If equality holds in (2.12), the permutation τ is said to be non-crossing ; in this case, the permutation τ −1γn (which is also non-crossing) is denoted by K(τ ) and is called the Kreweras complement of τ .
Asymptotic Freeness of Random Permutation Matrices from Gaussian Matrices
The action of such a permutation on an element of the n-dimensional binary cube is to XOR a single coordinate with a Boolean function of 2 other coordinates; there are 16n(n − 1)(n − 2) such permutations.
Simple Permutations Mix Even Better
Theorem 7. (Barenco et al. ) The permutation that ﬂips the n-th bit of input x if and only if the ﬁrst w bits of x are 1 can be implemented as a composition of O(w) permutations from Σ, as long as w ≤ n − 2.
Simple Permutations Mix Even Better
Each such path is deﬁned by composing simple permutations from Σ to achieve the permutation that acts on x ∈ {0, 1}n by ﬂipping coordinate c if the restriction of x to Cj is β .
Simple Permutations Mix Even Better
The second point is that some of the simple permutations used (σ1 and some of the permutations in φ) do not use three indices.
Simple Permutations Mix Even Better
Note that the set Σ of simple permutations is closed under conjugation by permutations from Sn, because this just relabels the indices.
Simple Permutations Mix Even Better
The permutation in input is chosen uniformly at random from the class of all possible permutations.
Online Permutation Routing in Partitioned Optical Passive Star Networks
One recalls that an involution is a permutation π with the additional property that π2 = I, where I denotes the identity permutation.
Correlation functions for random involutions
To complete the proof we must show that every non-crossing annular permutation arises from a pair of non-crossing circular half-permutations.
Orthogonal Polynomials and Fluctuations of Random Matrices
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