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Permutation matrix

Permutation In FFPA notation, one can write the cycles induced by the permutation; that is, one takes any element (say 1); then the element the first one is being sent to (here 2); then the element this one is sent to (here 5), and so on, until one comes back to the first. Of course, the same permutation could be written as (4 3)(2 5 1), or any other variant, but the "canonical" form for a permutation places the lowest-numbered position in each cycle first in that cycle and then orders the cycles by increasing first element. An even permutation is a permutation which can be expressed as a product of even number of transpositions, and the identity permutation is a even permutation as it equals (1 2)(1 2). www.ebroadcast.com.au /lookup/encyclopedia/pe/Permutation.html   (535 words)

Permutation Encyclopedia Article @ 209.68.55.237 ()   (Site not responding. Last check: 2007-10-29) 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. 209.68.55.237 /encyclopedia/Permutation   (1258 words)

Permutation: Encyclopedia topic   (Site not responding. Last check: 2007-10-29) That is, a permutation is simply an ordered sequence (sequence: Serial arrangement in which things follow in logical order or a recurrent pattern) with no two elements the same, drawn from a fixed set of symbols, and of maximum length. An even permutation (even permutation: more facts about this subject) 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). Permutation group (Permutation group: in mathematics, a permutation group is a group g whose elements are permutations... www.absoluteastronomy.com /reference/permutation   (1939 words)

Permutation   (Site not responding. Last check: 2007-10-29) In modern mathematical terminology, such as that used in professional combinatorics, the word permutation is now rarely used except in the case r=n. Some of the older textbooks do look at permutations an alternative way (essentially as assignment operations); the difference could be used to illustrate one way in which functional programming and imperative programming differ. In cycle notation, one can write the cycles induced by the permutation; that is, one takes any element (say 1); then the element the first one is being sent to (here 2); then the element this one is sent to (here 5), and so on, until one comes back to the first. bopedia.com /en/wikipedia/p/pe/permutation.html   (649 words)

Josephus permutation - Wikipedia, the free encyclopedia The order which is removed is the (m, n)-Josephus permutation. There are O(n) time algorithms for generating Josephus permutations. For the various variations it is possible to find a closed form, enabling the player of such a "game" to determine the position that will be the last one to be eliminated (since, according to tradition, the players eliminate one another, the player in the last position is the survivor). en.wikipedia.org /wiki/Josephus_permutation   (202 words)

Josephus permutation   (Site not responding. Last check: 2007-10-29) In computer science, the Josephus permutation is defined as follows. Suppose n people are arranged in a circle and we are given a positive integer m The Josephus permutation algorithm can be written in O(n) time. bopedia.com /en/wikipedia/j/jo/josephus_permutation.html   (49 words)

iqexpand.com   (Site not responding. Last check: 2007-10-29) A permutation, also called an "arrangement number" or "order," is a rearrangement of the elements of an ordered list S into a one-to-one correspondence with S itself. Permutation originated from the desire to unite scientific and linguistic disciplines to produce clear, accurate, and effective technical documents. Permutation's approach is based on our years of... permutation.iqexpand.com   (1744 words)

josephus   (Site not responding. Last check: 2007-10-29) Josephus wrote an account of the war addressed to the Jewish community in Mesopotamia in Aramaic which is now dead. At the end of the Antiquities is an autobiographical section in defense of Josephus's own conduct at the end of the war when he cooperated with the Roman forces of Vespasian. Josephus's Against Apion is a defense of Judaism against classical religion and philosophy stressing the antiquity of Judaism and its scriptures against what Josephus pointed out was the relatively more recent traditions of the Greeks. www.fact-library.com /josephus.html   (322 words)

Permutation: Facts and details from Encyclopedia Topic   (Site not responding. Last check: 2007-10-29) the term permutation (of a set) is now reserved for a bijective map[for more facts and a summary of this subject, click this link] (bijection[for more facts and a summary of this subject, click this link]) from a finite set onto itself, Exception Handler: No article summary found. Josephus permutation (In computer science, the josephus permutation is defined as follows....) Permutation group (In mathematics, a permutation group is a group g whose elements are permutations of a given set m,...) www.absoluteastronomy.com /ref/permutation   (3422 words)

Infogine permutation info page   (Site not responding. Last check: 2007-10-29) Counting permutations In this section only, the traditional definition is used: a permutation is an ordered list without repetitions, perhaps missing some elements. Special permutations If we think of a permutation that "changes" the position of the first element to the first element, the second to the second, and so on, we really have not changed the positions of the elements at all. Numbering permutations Factoradic numbers can be used to assign unique numbers to permutations, such that given a factoradic n, one can quickly find the corresponding permutation. www.infogine.com /computer/p/permutation.html   (2830 words)

OSB: Permutations combinations   (Site not responding. Last check: 2007-10-29) Types of file The various permutations and combinations of the five different types of data that may be presented in a computer file distributed between three or A permutation of the alphabet of 26 letters is a literal 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''. As explained in a previous section, in abstract algebra and other mathematical fields, the term ''permutation (of a set)'' is now reserved for a bijective (bijection) from a finite set onto itself. www.onesimpleband.com /coffee-espresso-making/makers-mug-combinations/permutations-combinations.html   (1841 words)

Combinatorial Algorithms   (Site not responding. Last check: 2007-10-29) An arrangement of these objects in a row is called a permutation of the objects. There are six permutations of 1, 2, 3: 123, 132,213, 231,312,321. A permutation can also be regarded as a rearrangement, i.e. users.forthnet.gr /ath/andreasv/html/permutations.htm   (397 words)

Permutation   (Site not responding. Last check: 2007-10-29) A permutation is an ordered Sequence containing each symbol from a set once and only once; neither "1, 2, 2, 3, 4, 5, 6" nor "1, 2, 4, 5, 6" are permutations. The assignment/substitution difference is then illustrative of one way in which Functional programming and Imperative programming differ - pure functional programming has no assignment mechanism. It is licensed under the GNU free documentation license. pda.molinu.com /wiki/en/pe/Permutation.htm   (1487 words)

[No title]   (Site not responding. Last check: 2007-10-29) Given two positive integers n and k, compute the last element of the Josephus permutation J(n,k) by using n processes communicating in a ring. The Roman/Palestinian historian Flavius Josephus recorded a mass suicide at Masada (73 C.E.) of which he was the only survivor. n) of the people as they are killed form the Josephus permutation J(n,k); the identifier of the last person standing is considered the last element of the permutation. www.cs.engr.uky.edu /~raphael/courses/CS570/asg.2.html   (599 words)

Permutation - Permutation   (Site not responding. Last check: 2007-10-29) A model with flavor-triplet Higgs scalars phi _{i} (i=1,2,3) is investigated under a permutation symmetry S_{3} and its symmetry breaking. Given a permutation of N different objects, map it uniquely to an integer from 0 to N!-1, and vice versa. Cherchez l'argent: The latest permutation in the tale of Carla "Coach" Martin suggests that it wasn't incompetence, or overzealousness, that led her to violate the court's order and supply trial transcripts to FAA witnesses. martial-art.misinformation.be /Mixed_radix/Permutation   (420 words)

Permutation -   (Site not responding. Last check: 2007-10-29) For other uses of this term, see Permutation (disambiguation). Note that if objects 1,2,3,4,5 are rearranged into the order 2,5,4,3,1, two permutations are involved: (1 5 2) (3 4) mapping the original to the final position of each object, and (1 2 5) (3 4) mapping the old to the new object at any position. Notation (1 5 2) implies that 3 and 4 are not changed. www.gurgaongrid.com /mediawiki/index.php/Permutation   (1475 words)

Permutation - Permutation In the latter case, the number of permutations is (n + r − 1)r. If we have some permutation called P, we can describe a permutation, written P−1, which undoes the action of applying P. In essence, performing P then P−1 is the same as performing the identity permutation. Note that R could be P or Q. The product of P and Q is defined to be the permutation R. For more, see symmetric group and permutation group. ivanna.clubblogs.com /ivanna/Altar/Permutation   (1294 words)

abstr01 Ledah Casburn and Tuyet-Linh Phan considered the Josephus Problem from a new perspective. Sarah Breede and Christy Finch considered a variation of the classical Josephus Dilemma. Instead of killing all but one person, they considered killing exactly half of the group, which is distinct from the other half. www.users.muohio.edu /porterbm/sumj/2001/abstr01.html   (710 words)

permutation   (Site not responding. Last check: 2007-10-29) ---- In mathematics, the concept of a permutation expresses the idea that objects that can be distinguished may be arranged in various different orders. (n − r + 1) different permutations of r objects, taken from a pool of n objects, exist. Zdnet calls the development as something of "a new permutation in Web search," with the idea being to compress around one million gigabytes into just 40... www.33beat.com /permutation.html   (1827 words)

[No title]   (Site not responding. Last check: 2007-10-29) Describe as precisely as possible (think you are writing to a friend who is deaf and blind) the Josephus game. List three aspects of the Josephus game which are irrelevant to the game. Write all 24 permutations on the four symbols {Q, R, S, T} using the one-line (cycle) notation. www.nd.edu /~mario/classes/math103/homework.html   (445 words)

Josephus Permutation   (Site not responding. Last check: 2007-10-29) The Josephus Problem is defined as follows : Use the + and - buttons to vary the value of m. The Josephus button displays the permutations for n=1 to n=100. www.wou.edu /~burtonl/josephus.html   (75 words)

I can't solve these.   (Site not responding. Last check: 2007-10-29) The order in which the people are removed from the circle defines the (n,m)-Josephus permutation of integers 1,2,...,n. Describe an O(n lg n)-time algorithm that, given integers n and m, outputs the (n,m)-Josephus permutation. Of course, my question asks for a constant-time algorithm (or a lower-bound for the algorithm) for the last number in a (n,8)-Josephus permutation. www.varatek.com /scott/not_solved.html   (271 words)

Intro to Algorithms: CHAPTER 15: AUGMENTING DATA STRUCTURES   (Site not responding. Last check: 2007-10-29) The order in which the people are removed from the circle defines the (n, m)-Josephus permutation of the integers 1, 2,. For example, the (7, 3)-Josephus permutation is < 3, 6, 2, 7, 5, 1, 4 >. Describe an O(n 1g n)-time algorithm that, given integers n and m, outputs the (n, m)-Josephus permutation. www.comp.nus.edu.sg /~liusheny/clrs/book6/chap15.htm   (5057 words)

Works Citing the On-Line Encyclopedia of Integer Sequences Marcelo Aguiar (Texas A&M University) and Frank Sottile (University of Massachusetts at Amherst), math.CO/0203282: Structure of the Malvenuto-Reutenauer Hopf algebra of permutations. Barcucci, A. Del Lungo, E. Pergola and R. Pinzani, From Motzkin to Catalan permutations, Discrete Mathematics, 217 (2000), 33-49. West, Permutation trees and the Catalan and Schr=F6der numbers, Discrete Math., 146: 247-262 (1995). www.research.att.com /~njas/sequences/cite.html   (9101 words)

[No title]   (Site not responding. Last check: 2007-10-29) function x = josephus (n, m, k) %% JOSEPHUS returns the position X of the K-th man to be executed. % % Discussion: % % The classic Josephus problem concerns a circle of 41 men. % % The process may be regarded as generating a permutation of % the integers from 1 to N. The permutation would be the execution % list, that is, the list of the executed men, by position number. www.csit.fsu.edu /~burkardt/m_src/subset/josephus.m   (256 words)

Download Joseph - The Flavius Josephus Permutation Problems 1.10 - Joseph - The Flavius Josephus Permutation Problems ... Download Joseph - The Flavius Josephus Permutation Problems 1.10 - Joseph - The Flavius Josephus Permutation Problems is a free and useful utility that will calculate permutations - Softpedia Joseph - The Flavius Josephus Permutation Problems is a free and useful utility that will calculate permutations. Softpedia guarantees that Joseph - The Flavius Josephus Permutation Problems 1.10 is www.softpedia.com /get/Others/Home-Education/Joseph-The-Flavius-Josephus-Permutation-Problems.shtml   (341 words)

FYI: TETRAGRAMMATON - Jewish Encyclopedia The quadriliteral name of G-d, yod/hay/vav/hay, which is thus referred to in Josephus, in the Church Fathers, in the magic papyri, and in the Palestinian Talmud {Yoma 40a below}, whence it has passed into the modern languages. All the critics have failed to perceive that the name "Yao" was derived from the same source as "yaoue," namely, from Gnosticism and magic, in which Jews, Christians, and heathen met. "Yahu" was in fact used in magic, as is clear from the "Sefer Yezirah," which shows many traces of Gnosticism; in the cosmology of this work the permutation of the letters yod/hay/vav furnishes the instruments of the Creation. www.iahushua.com /ST-RP/tetje.htm   (1883 words)

ACSU Programming Competition, Spring 1997 This problem reduces to the following: Given n (the number of people in the circle), and k (the number of people the punch is passed), determine l (the last person left alive) assuming that the punch starts at person 1. The order in which the people die enforces a permutation on the integers 1 to n. I am looking for a closed-form solution to this problem. www.cs.cornell.edu /people/mpal/contest/97sp   (640 words)

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