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Topic: Permutation

Related Topics

Signature (permutation)

Permutation matrix

Permutation group

Cyclic permutation

Combinatorics

Change ringing

Cyclic group

Group (mathematics)

Special unitary group

Formal language

Chromatic polynomial

Chinese remainder theorem

Square root

List of matrices

Determinant

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	PlanetMath: permutation
		A permutation can also be seen as a bijective function of a set into itself.
		Using the function approach, it can be proved that any permutation can be expressed as a composition of disjoint cycles and also as composition of (not necessarily disjoint) transpositions.
		This is version 3 of permutation, born on 2001-10-20, modified 2002-02-19.
	planetmath.org /encyclopedia/Permutation.html (175 words)

	Permutation - Wikipedia, the free encyclopedia
		In mathematics, especially in abstract algebra and related areas, a permutation is a bijection from a finite set X onto itself.
		An even permutation is a permutation which can be expressed as the product of an even number of transpositions, and the identity permutation is an even permutation as it equals (1 2)(1 2).
		An odd permutation is a permutation which can be expressed as the product of an odd number of transpositions.
	en.wikipedia.org /wiki/Permutation (1473 words)

	Permutation (Site not responding. Last check: 2007-10-21)
		A permutation of the alphabet of 26 letters is a string of length 26 containing each letter just once; and it is clear that this definition works for any alphabet of N letters, with strings of length N.
		That is, a permutation is simply an ordered sequence with no two elements the same, drawn from a fixed set of symbols, and of maximum length.
		It should be noted that in modern usage, the default meaning of the term "permutation" is synonymous with bijection, unless stated otherwise.
	hallencyclopedia.com /Permutation (1814 words)

	Permutation cipher - Wikipedia, the free encyclopedia
		In classical cryptography, a permutation cipher is a transposition cipher in which the key is a permutation.
		To apply a cipher, a random permutation of size e is generated (the larger the value of e the more secure the cipher).
		With the different possible key sizes different possible permutations are tried to find the permutation which results in the highest number of frequent bigrams and trigrams as found in the underlying language of the plaintext.
	en.wikipedia.org /wiki/Permutation_cipher (339 words)

	Problem #3: Permutation Inversion Tables (Site not responding. Last check: 2007-10-21)
		For example, the six permutations of the integers { 1, 2, 3 } are: 1 2 3, 1 3 2, 2 1 3, 2 3 1, 3 1 2, and 3 2 1.
		There are several methods used to represent a permutation of the integers { 1, 2, 3,..., n }, one of which is to show the permutation directly as was done above for each of the six permutations of { 1, 2, 3 }.
		A permutation determines a unique inversion table; furthermore, given the inversion table it is possible to reconstruct the associated permutation.
	www.acm.inf.ethz.ch /ProblemSetArchive/B_US_EastCen/1984/permute.htm (451 words)

	Overlay input images to generate gray level permutation codes
		Each entry in the permutation table stores a permutation code, a count of the number of pixels in the output image that have been assigned that permutation code, and a list of the input image pixel values that comprise that permutation.
		Each entry in the permutation table stores a permutation code, a count of the pixels in the output image that are assigned to the permutation code, and a list of the gray levels that compose the permutation.
		Each permutation record contains a permutation code, a count of the number of times the permutation code was assigned to a pixel in the output image, and the corresponding pixel values from the input images that define the permutation.
	dbwww.essc.psu.edu /lasdoc/user/intersect.html (1731 words)

	Random Permutation Generation
		A permutation tree of n items is generated recursively; at the root all n items are available for selection, so the root has n edges of different colors leading to n subtrees.
		Counting the number of paths in a permutation tree is fairly straightforward; at the root n paths emerge, and each of these n paths splits into n-1 paths at the subtrees of the root.
		A permutation is simply a rearrangement of all n items; a permutation is equivalent to a kpermutation when k equals n.
	www.techuser.net /randpermgen.html (1694 words)

	Permutation Group Actions
		Given a permutation g belonging to a group G and a G-set Y, construct the fixed-point set of g in its action on Y. In the case in which Y is the natural G-set, Y may be omitted.
		Given a transitive permutation group G with natural G-set X and a G-invariant partition P of X, construct the group induced by the action of G on the blocks of P. In the second form, P is specified by giving a single block of the partition.
		Given a transitive permutation group G with natural G-set X and a G-invariant partition P of X, construct the kernel of the action of G on the blocks of P. In the second form, P is specified by giving a single block of the partition.
	magma.maths.usyd.edu.au /magma/htmlhelp/text278.htm (3510 words)

	Randomization Tests
		A better permutation test might be to define two permutation blocks: one would be the fertilized lakes, and the other would be the unfertilized lakes.
		The permutation test would be identical to the preceding example, except one would only reshuffle observations within fertilized lakes, and separately within unfertilized lakes.
		Permutation blocks are fairly simple to define, especially in the context of partial ordination.
	www.okstate.edu /artsci/botany/ordinate/permute.htm (907 words)

	Permutation: Bach C-Minor Fugue and Pärt "Fratres"
		In the mathematical sense, "permutation" is a process in which an array of numbers is arranged in all of its possible subsets.
		Permutation is, in short, a sure way to achieve the goal of saturating a composition with motive without textural redundancy.
		And, if there are four clockwise permutations of the p-form of the year, then there are, likewise, four COUNTERCLOCKWISE rotations of the i-form of the year, for a total of eight permutations, all more-or-less dictated by which direction the earth orbits the sun...forward or backward.
	jan.ucc.nau.edu /~tas3/perm.html (3564 words)

	Construction of Orthogonal Arrays and Covering Arrays Using Permutation Groups
		Permutation vectors which extend the formulation to groups with orders of powers of m are defined for values of m which are primes and prime powers.
		Additional arrays of permutation vectors, for m=7, m=8, and m=9, are included in an appendix.
		Consequently, this transformation is a permutation of levels of a column, which results in an orthogonal array with the same parameters.
	home.att.net /~gsherwood/cover.htm (5848 words)

	Permutations and combinations - Topics in precalculus
		For example, if twelve different things are permuted, then the number of their permutations is 479,001,600.
		That is, the number of permutations of 4 different things taken 4 at a time is 4!.
		This is the number of permutations of 10 different things taken 4 at a time.
	www.themathpage.com /aPreCalc/permutations-combinations.htm (1049 words)

	permutation from FOLDOC (Site not responding. Last check: 2007-10-21)
		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.
		What the football pools call a "permutation" is not a permutation but a combination - the order does not matter.
	foldoc.org /?permutation (137 words)

	Amon Tobin: Permutation: Pitchfork Review (Site not responding. Last check: 2007-10-21)
		His rhythms draw on bossa nova and samba while he samples creepy string arrangements, standup bass, vicious vibes, spastic horn solos and piano loops, taking "out of control" to the next level.
		Permutation has Tobin putting a heavier piece of wax on the turntable than his ground-breaking full-length debut, 1997's Bricolage.
		Permutation's final note rang throughout the misty streets, the echo of a chime and quietly tapped snare.
	www.pitchforkmedia.com /record-reviews/t/tobin_amon/permutation.shtml (262 words)

	Permutations
		A permutation is a 1-1 correspondence of a set V onto itself: f: V
		A permutation is a way of counting elements in a set.
		Most often for the sake of convenience, when discussing permutations, indices is all that's considered and the symbol v for the set's element is omitted.
	www.cut-the-knot.org /do_you_know/permutation.shtml (455 words)

	Description of permutation (Site not responding. Last check: 2007-10-21)
		constructor for the permutation class p = permutation(n) --- create a new (identity) permutation on 1:n p = permutation(vec) --- create a new permutation based on the array vec (which should be a permutation of 1:n).
		size size(p) returns the number of elements permuted and the number of cycles.
		0001 function p = permutation(n) 0002 % constructor for the permutation class 0003 % p = permutation(n) --- create a new (identity) permutation on 1:n 0004 % p = permutation(vec) --- create a new permutation based on the array vec 0005 % (which should be a permutation of 1:n).
	mts.jhu.edu /~ers/matgraph/html/matgraph/@permutation/permutation.html (153 words)

	Encyclopedia: Permutation (Site not responding. Last check: 2007-10-21)
		In mathematics, a set can be thought of as any collection of distinct things considered as a whole.
		Combinatorics is a branch of mathematics that studies collections (usually finite) of objects that satisfy specified criteria.
		Permutation article - Permutation permutation (music) mathematics change ringing alphabet string - What-Means.com
	www.nationmaster.com /encyclopedia/Permutation (430 words)

	[ref] 41 Permutation Groups
		Permutation groups are groups and therefore all operations for groups (see Chapter Groups) can be applied to them.
		Such a known base makes it easier to test whether a permutation given as a word in terms of a set of generators is the identity, since it suffices to map the known base with each factor consecutively, rather than multiplying the whole permutations (which would mean to map every point).
		Permutation groups of large degree (usually at least a few 10000) can pose a challenge to the heuristics used in the algorithms for permutation groups.
	www.math.sunysb.edu /~sorin/online-docs/gap4r3/htm/ref/CHAP041.htm (4293 words)

	permutation (Site not responding. Last check: 2007-10-21)
		Note: A sort is a permutation where the items are arranged in some order.
		A derangement is a permutation where no item is in its original position.
		Paul E. Black, "permutation", from Dictionary of Algorithms and Data Structures, Paul E. Black, ed., NIST.
	www.nist.gov /dads/HTML/permutation.html (124 words)

	Problem I - Bangladesh 2001 Programming Contest
		There are some permutation generation techniques in Knuth’s book “The Art of Computer Programming - Volume 1”.
		Following this rule you have to generate all the permutation for a given set of characters.
		That is the permutation sequence for abc and bca will not be the same.
	acm.uva.es /p/v100/10063.html (232 words)

	Permutation Equivalent Codes (Site not responding. Last check: 2007-10-21)
		Now choose a permutation of the columns of the new generator matrix so that these columns are moved to the order that produces
		These three permutations generate a simple, non-abelian group of order 168, which turns out to be a very special group,
		The ``stabilizer" of the code is the set of all elements of the symmetric group which fix the code (as a set), i.e., the permutation automorphism group of the code.
	www.math.unl.edu /~bbockelm/coding-notes/node7.html (618 words)

	Renfrow, James Thomas (1969-04-02) A study of rank four permutation groups. ...
		A rank 4 group is a finite transitive permutation group acting on a set [Omega] such that the subgroup fixing a letter breaks up [Omega] into 4 orbits.
		Intersection matrices are used to obtain relations between the lengths of the four orbits associated with a rank 4 representation and the degrees of the irreducible characters in the permutation character of the representation.
		It is shown that two orbits of the representation are paired if and only if two of the characters are complex conjugates of one another.
	etd.caltech.edu /etd/available/etd-09272002-154545 (224 words)

	Permutation routing in hypercubic networks
		It is known that all the hypercubic MIN have equivalent end-to-end permutation routing properties.
		Similarly to meshes, if a permutation is known beforehand globally, we can precompute off-line paths for routing such that the communication becomes contention-free and the permutation can routed in the optimal number of communication steps.
		The permutations are not necessarily complete since G is not necessarily d-regular and all the nodes do not necessarily use all their channels in every communication step.
	www.cs.wisc.edu /~tvrdik/10/html/Section10.html (2889 words)

	PERMUTATION GROUPS
		An important class of groups are permutation groups.
		One reason for their importance is that every group may be represented as a group of permutations on a suitable set.
		we mean that the permutation maps 1 to 2, maps 2 to 3 and maps 3 to 1.
	www.math.csusb.edu /notes/advanced/algebra/gp/node6.html (312 words)

	Tech Reports: HPL-97-59R1: Data Dependent Optimizations for
		Permutation warping may use any one pass filter kernel, an example of which is trilinear reconstruction, an advantage over the shear warp approach.
		Because permutation warping has good scalability characteristics, it proves to be a superior approach for massively parallel computers when image fidelity is a required feature.
		We have provided further evidence for the utility of permutation warping as a scalable, high fidelity, and high performance approach to parallel volume visualization.
	www.hpl.hp.com /techreports/97/HPL-97-59R1.html (234 words)

	PlanetMath: signature of a permutation
		"signature of a permutation" is owned by rspuzio.
		Cross-references: induction, identity map, clear, relation, totally ordered, odd, transposition, multiplicative group, homomorphism, permutation group, permutations, group, finite
		This is version 6 of signature of a permutation, born on 2003-02-26, modified 2004-10-31.
	planetmath.org /encyclopedia/Signature2.html (118 words)

	next_permutation
		into the lexicographically smallest permutation [2] and returns
		The postcondition is that the new permutation of elements is lexicographically greater than the old (as determined by
		[2] Note that the lexicographically smallest permutation is, by definition, sorted in nondecreasing order.
	www.sgi.com /tech/stl/next_permutation.html (279 words)

	Various ways to define a permutation
		One way to represent a permutation f is by listing its values at i = 1,...,n: {f(1),f(2),...,f(n)}.
		A more explicit way to present a permutation is to use a two row table (a row per a copy of N
		In the applet, every permutation is also presented as a product of cycles.
	www.cut-the-knot.org /do_you_know/Perm.shtml (488 words)

	Intersubunit circular permutation of human hemoglobin -- Sanders et al. 100 (1): 299 -- Blood
		The circularly permuted hemoglobin was eluted with a linear gradient
		Figure 3 is a schematic of the linear amino acid sequence and folded structure of the circularly permuted hemoglobin (CpHb).
		as the new amino termini for the circularly permuted
	www.bloodjournal.org /cgi/content/full/100/1/299 (4781 words)

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