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Topic: Cyclic permutation

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Permutation

Permutation group

Permutations and combinations

Symmetric group

	Cyclic permutation - Wikipedia, the free encyclopedia
		A permutation P over a set S with k elements is called a cyclic permutation with offset t iff
		A permutation is called a cyclic permutation iff it will be constructed with exactly 1 cycle.
		Note: Every cyclic permutation of definition type 3 may be seen as an union of a cyclic permutation of definition type 2 and some fixed points.
	en.wikipedia.org /wiki/Cyclic_permutation (300 words)

	cylic quadralerals
		A cyclic quadrangle or cyclic quadrialteral is a quadrilateral for which a single circle passes through all four vertices.
		The midpoint of the line segment between the center of the circle, and the anti-center is the Centroid, or center of Gravity of the four vertices.
		The center of this "orthic cyclic quadrilateral" is the reflection of the circumcenter of the original quadrilateral in the anti-center.
	www.pballew.net /cycquad.html (1589 words)

	Wolfram Research, Inc.
		A permutation is a rule for rearranging a finite collection of elements.
		All permutations are not cycles, but it is a basic fact that any permutation can be decomposed into a product of cycles.
		The sublist is treated cyclically so the last element is thought of as being "before" the first.
	documents.wolfram.com /v3/AddOns/DscM_Permutations-.html (154 words)

	PET
		Now every permutation is uniquely expressible as a composition of cyclic permutations on mutually exclusive subsets of the elements of X.
		Thus the permutation (5.1) is the composite of one cyclic permutation of length 1, two cyclic permutations of length 3, and one cyclic permutation of length 4, the cyclic permutations acting on disjoint subsets of the set X.
		The group G of symmetries is a group of order 8, which we describe by permutations of the set of vertices {1,2,3,4}.
	www.mi.sanu.ac.yu /vismath/hil/ped5.htm (805 words)

	Alternating groups.
		If we insted would wish a cyclic permutation, (pqr...s) to be a set of alternations against a certain element, say a, then we
		This means that all permutations could be revritten as alternations, and that all these altenations could be done against one element.
		A1 gives us that a circular permutation involving n elements will be possible to do in n-1 alternations.
	hemsidor.torget.se /users/m/mauritz/math/alg/alt.htm (274 words)

	Octahedral Group
		permutations will also be left as an exercise.
		This can be decried as the cyclic permutation (13)(24)(56), if we name the corners as above.
		These reflections could be decried as permutation cycles of two elements, and we get (13), (24) and (56).
	hemsidor.torget.se /users/m/mauritz/math/alg/oct.htm (463 words)

	Music and Mathematics
		The set of all such permutations of A is a group under the binary operation composition of mappings, called the “symmetric group.” If A is finite with n elements, e.g.
		The map from G to SA (the group of all permutations of the carrier set A) defined by gàsg is a homomorphism.
		The sets of numbers that appear in the individual cycles of the cyclic decomposition of some permutation s are the orbits of the cyclic subgroup generated by s, .
	faculty.washington.edu /jrahn/5752004.htm (5226 words)

	ABSTRACT ALGEBRA ON LINE: Groups
		The set of all permutations of a set S is denoted by Sym(S).
		If a permutation is written as a product of transpositions in two ways, then the number of transpositions is either even in both cases or odd in both cases.
		A permutation is called even if it can be written as a product of an even number of transpositions, and odd if it can be written as a product of an odd number of transpositions.
	www.math.niu.edu /~beachy/aaol/groups.html (1115 words)

	[No title] (Site not responding. Last check: 2007-09-07)
		It turns out there is a rather large literature on generation of permutations, and the methods illustrated here only begin to scratch the surface.
		We can suppose a given permutation is cyclic, since with relabelings the complete inductive hypothesis can be applied to each cycle in a product of nonempty disjoint cycles.
		For the cyclic permutation of 1...n-1, if we wish to insert n in the cycle at -> i -> n -> j we can take, by induction, [ product for case n-1 taking i->j ] (n,j) We take s_i to be the ith factomial digit of the argument passed in.
	barnyard.syr.edu /quickies/perms.c (399 words)

	3-D Crystals III
		These six permutations are, in addition to representing all the symmetries of the Equilateral Triangle, at the same time the direct symmetries of the Trigonal Bipyramid where p and q represent the apices of this bipyramid, i.e.
		Said differently, the permutation q p c a b of the elements of the group does not preserve structure, and so does not represent one of its automorphisms.
		Of course the group table according to that permutation is a perfectly correct group table of our group, because we may reshuffle our elements at will (and reshuffle their products accordingly) to create a table.
	home.hetnet.nl /~turing/d3_lattice_3.html (3195 words)

	[No title]
		The intersection of a quadric surface with a sphere.
		NOS A yellow liquid with limited solubility in water; boiling point is 145-146°C; used as an herbicide to control weeds in sugarbeets, spinach, and table beets.
		One of two cyclic hydrocarbons with three double bonds; the two forms are stereoisomeric; used to make nylon-6 and nylon-12.
	www.accessscience.com /Dictionary/C/C64/DictC64.html (2282 words)

	Cycle notation
		The most common notation for a permutation is the ``cycle notation".
		Lemma 4.4.8 A cyclic permutation is even if and only if the length of its cycle is odd.
		Use the cycle notation to determine the permutations of the facets (a)
	web.usna.navy.mil /~wdj/book/node155.html (543 words)

	Consolidating critical binding determinants by noncyclic rearrangement of protein secondary structure -- Tabtiang et ...
		N-terminal sequence is shifted to the C terminus of the permuted
		The gene for the permuted pArc molecule was
		We reengineered the sequence to encode a permuted single-chain
	www.pnas.org /cgi/content/full/102/7/2305 (2387 words)

	Algebraic Combinatorics -- Cycle decomposition
		a cyclic permutation or a cycle if and only if it can be written in the form
		The notation for a cyclic permutation is not uniquely determined, since
		There are some more examples for the cycle decomposition of a permutation.
	www.mathe2.uni-bayreuth.de /frib/html2/book/hyl00_22.html (314 words)

	[No title]
		By a permutation representation N : G GL(n, F) we understand a linear representation together with a basis X = {x 1,.
		It turns out that the image of the transfer for cyclic pgroups is a prime ideal of height at most n - k, where k denotes the number of orbits of a permutation basis.
		Hence for arbitrary permutation groups not even the weaker version (where the restriction to Chern classes of degree divisible by p is omitted) of Theorem 4.2 is valid.
	hopf.math.purdue.edu /Neusel/bertin.txt (3209 words)

	Energy Citations Database (ECD) - Energy and Energy-Related Bibliographic Citations
		An important property of the Z{sub 2}xZ{sub 2} orbifold is the cyclic permutation symmetry between the three twisted sectors.
		If preserved in the three-generation models the cyclic permutation symmetry results in a family universal anomalous U(1){sub A}, which is instrumental in explaining squark degeneracy, provided that the dominant component of supersymmetry breaking arises from the U(1){sub A} D term.
		Interestingly, the contribution of the family-universal D{sub A} term to the squark masses may be intrafamily nonuniversal, and may differ from the usual (universal) boundary conditions assumed in the MSSM.
	www.osti.gov /energycitations/product.biblio.jsp?osti_id=20216982 (373 words)

	Uniformly Most Powerful Cyclic Permutation Invariant Detection For Discrete-Time Signals (ResearchIndex) (Site not responding. Last check: 2007-09-07)
		Abstract: The uniformly most powerful invariant test is derived for the problem of detecting a signal with unknown location in a sequence of noise.
		This test has the property that for each possible signal location it has the greatest power of all tests which are invariant to cyclic permutations of the observations.
		The test is compared to the generalised likelihood ratio test, which is more typically used for this detection problem.
	citeseer.ist.psu.edu /395606.html (307 words)

	[ref] 45 Group Libraries
		Two permutations groups of the same degree are considered to be equivalent, if there is a renumbering of points, which maps one group into the other one.
		As all groups are stored by presentations, a permutation representation is obtained by coset enumeration.
		means that a nontransitive permutation representation is available which acts on two orbits of size 5 and 16 respectively.
	www.math.colostate.edu /manuals/gap/CHAP045.htm (3533 words)

	Quasi-cyclic Goppa codes. (Site not responding. Last check: 2007-09-07)
		Some semi-monomial automorphisms of GRS codes that are not permutations of the support induce a permutation of the subfield-subcodes [1,2].
		T.P. Berger, ``Cyclic Alternant codes induced by an automorphism of a GRS code," Finite fields: Theory, Applications and Algorithms, (R. Mullin and G. Mullen Eds).
		T.P. Berger, ``On the cyclicity of Goppa codes, parity-check subcodes of Goppa codes and extended Goppa codes," to appear in Finite Fields and their Applications.
	www.unilim.fr /pages_perso/thierry.berger/ISIT2000.html (473 words)

	Powers of a cyclic permutation and their cycle types (Site not responding. Last check: 2007-09-07)
		Powers of a cyclic permutation and their cycle types
		Please enter n, the length of a cyclic permutation!
		For starting computation of all powers of a cycle of length n, and all the cycle types of these powers, press the button
	www.uni-graz.at /~fripert/fga/k1pow.html (50 words)

	node4
		or as long as they satisfy the cyclic permutation rule.
		The cyclic permutation rule is any triplet of vectors satisfying the relations below and are said to satisfy the cyclic permuation rule.
		Proper coordinate transformations are those that leave the cyclic order undisturbed.
	www.uic.edu /classes/eecs/eecs401/Week1/node4.html (140 words)

	32nd IMO shortlist 1991/24 solution (Site not responding. Last check: 2007-09-07)
		Find all odd integers n > 1 for which there is at least one permutation a
		As usual take cyclic indices, so that an index of n+1 means 1, an index of n+2 means 2 etc. Put b
		Now suppose we have a permutation which works for n = 4k - 1.Then 1 + 2 + 3 +...
	www.kalva.demon.co.uk /short/soln/sh9124.html (202 words)

	autocay (Site not responding. Last check: 2007-09-07)
		x^{-1} is in X whenever x is in X), and a cyclic permutation p on X, a Cayley map CM(G,X,p) is a 2-cell embedding of the Cayley graph C(G,X) into an orientable surface with the same local orientation p at every vertex.
		A map-automorphism A of a Cayley map M = CM(G,X,p) is an oriented-region-preserving permutation of the set of arcs of M.
		The group of all map-automorphisms of M, AutM, is always vertex-transitive thanks to the left-translation action of the underlying G.
	www.emba.uvm.edu /~archdeac/newlist/autocay.htm (343 words)

	[ref] 48 Group Libraries
		be a permutation group, acting transitively on a set of up to 30 points.
		All groups in the library are primitive permutation groups of the indicated degree.
		G is mapped to the permutation induced by its action on S.
	wwwmaths.anu.edu.au /research.programs/aat/GAP_manual/ref/CHAP048.htm (7621 words)

	Uniformly Most Powerful Cyclic Permutation Invariant Detection For Discrete-Time Signals (ResearchIndex)
		Abstract: The uniformly most powerful invariant (UMPI) test is derived for detecting a target with unknown location in a noise sequence.
		This test has the property that for each possible target location it has the greatest power of all tests which are invariant to cyclic permutations of the observations.
		The test is compared to the generalised likelihood ratio test (GLRT), which is commonly used as a solution to this detection problem.
	citeseer.ist.psu.edu /428773.html (266 words)

	[No title] (Site not responding. Last check: 2007-09-07)
		#include "perm/permrand.h" // random_cyclic_permutation() #include "perm/printperm.h" #include "fxtiomanip.h" #include "aux0/swap.h" #include "fxttypes.h" #include "perm/permq.h" // is_cyclic(),...
		#include "jjassert.h" #include "demo/nextarg.h" // NXARG() //% Random cyclic permutations.
		void visit(const ulong f, ulong n, ulong ct) // What to do with valid permutations*.
	www.jjj.de /fxt/demo/perm/permrandcyclic-demo.cc (41 words)

	[No title] (Site not responding. Last check: 2007-09-07)
		For example the method for constructing a cyclic permutation group is installed as follows (see~"prg:InstallMethod" in ``Programming in {\GAP}'' for the meaning of the arguments of `InstallMethod').
		With the exception of the symmetric and alternating group (which are represented as `SymmetricGroup' and `AlternatingGroup') the generators for these groups also conform to this paper with the only difference that 0 (which is not permitted in {\GAP} for permutations to act on) is always replaced by the degree.
		The message \begintt orbit size = 8 \endtt in the above example means that the available permutation representation is transitive and of degree 8, whereas the message \begintt orbit sizes = 5 + 16 \endtt means that a nontransitive permutation representation is available which acts on two orbits of size 5 and 16 respectively.
	www-groups.dcs.st-and.ac.uk /gap/Manuals/doc/build/grplib.msk (5404 words)

	Periodic Subwords in 2-Piece Words -- from Mathematica Information Center
		For k=3,4,6, W arises in a small cancellation group with single defining relation W=1.
		We assume W involves generators but not their inverses and does not have a periodic cyclic permutation (like XY...XYX for nonempty base word XY).
		We prove W or W written backwards equals ABCD where ABC, CDA are periodic words with base words of different lengths.
	library.wolfram.com /infocenter/Articles/5262 (107 words)

	Cycle decomposition
		a cyclic permutation or a cycle if and only if it can be written in the form
		We note that in this case the orbits of the subgroup generated by this permutation are the following subsets of
		.) Each permutation of a finite set can be written as a product of pairwise different disjoint cycles, e.g.
	www.mathe2.uni-bayreuth.de /frib/KERBER/h00/node21.html (243 words)

	Some programs for finite group actions in SYMMETRICA (Site not responding. Last check: 2007-09-07)
		The number of fixed points of a permutation
		The cycle type of the induced permutation on 2-sets
		The number of cycles of the induced permutation on 2-sets
	www.uni-graz.at /~fripert/fga/kerber1.html (98 words)

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