13. Symmetric groups 13.1 13.2 13.3 Cycles‚ disjoint cycle decompositions Adjacent transpositions Worked examples 1. Cycles‚ disjoint cycle decompositions The symmetric group Sn is the group of bijections of {1‚ . . . ‚ n} to itself‚ also called permutations of n things. A standard notation for the permutation that sends i −→ i is 1 2 3 1 2 3 ... ... n n Under composition of mappings‚ the permutations of {1‚ . . . ‚ n} is a group. The fixed points of a permutation
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GSB 9001 Lecture 1: What is communication? ‘Communication is the act of exchanging thoughts‚ messages‚ or information’ (de Janasz et al.‚ 2012‚ p.127) 1. It involves rich channels (face-to-face‚ telephone) 2. It involves lean channels (emails‚ texting‚ memos) Think through the implications of this difference in how we communicate‚ formally and informally. What is Listening? Listening is the process of taking in what we hear and mentally organising it; it involves: Sensing: hearing
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A Day in life of Alex Sander: Diyora Hitesh V Regd No. PA1110 Abstract Alex Sander is a new product manager at Landan care products inc. which has been acquired by a European Beauty company. Alex Sander is very talented and has rebranded two national products in one year. She knows very well when to launch product and she is smart enough to do things correctly. Sander is getting her
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The Freedom Riders: Terminators of Segregation Picture being on a bus traveling throughout the South in the midst of the Civil Rights Movement‚ knowing that when the bus arrives at the first stop‚ a group of activists against segregation called Freedom Riders will be viciously attacked by mobs of whites. Any advice to stay home and avoid the situation was disregarded by these brave Americans because defending the rights of African Americans was most important. Each rider understood that they
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The Free Rider Problem The free rider issue has become one of the most serious economic issues today. The free rider is a lazy type person who wants the benefits that others bring in without having to do the work. The free rider typically takes advantage of a public good. Living in a civilized society presents many opportunities for free riding‚ which we have yet to find a way to control. Economists regard the possibility for free riding as a problem for the free market‚ which usually leads
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After Nine days of constant grieving for her missing son‚ Michael‚ old Maurya is fallen into a restless sleep. Her daughter‚ Cathleen‚ is busy with household tasks‚ when another daughter‚ Nora‚ slips quietly into the kitchen with a bundle given her by the young priest. It contains part of the clothes taken from the body of a drowned man far in the north. They have been sent to the family for identification‚ since the clothes may belong to her missing brother. The girls go to open the
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Kolkata Knight Riders (Bengali: কলকাতা নাইট রাইডার্স) (often abbreviated as KKR) is the franchise representing Kolkata in the Indian Premier League‚ a Twenty20 cricket tournament. The team is led by Sourav Ganguly‚ and coached by Dav Whatmore. Sourav Ganguly is the team ’s Icon Player. The official theme of the team is Korbo‚ Lorbo‚ Jeetbo Re (Bengali for We will do it‚ Fight for it‚ Win it) and the official colors are purple and gold. As per the recent study done by a UK based brand valuation company
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Portfolio Management Case 1: Alex Sharpe’s Portfolio Executive Summary As Alex Sharpe’s consultant‚ we recommend a portfolio of 78% S&P 500 and 22% of R.J Reynolds. This portfolio will generate an annual expected return of 8.86% (significantly higher than the index return 6.29%)‚ while the risk increases by only less than 10%. In Qualitative Analysis‚ we find that tobacco industry tends to move with the market less than the toy industry‚ which indicates that R.J Reynolds can diversity the
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the world suddenly seem more real and cruel? In Claire Anderson-Wheeler’s short story‚ “Vernissage”‚ we hear about Alex who is suddenly faced with all these questions he cannot answer. In the story we meet Alex who lives with his parents‚ who have been married probably for a lot of years‚ and it is starting to show in the way they talk to each other. Through the story we follow Alex and only see and experience what he does. The story is written with a 3rd person narrator but an omniscient one‚ because
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tie in with Part One” worksheets‚ the wording and/ or sub questions have been changed. These similar ones can also be used in the same class as additional practice to make sure students answer exactly the question that is given. 62 Written by Alex Case for UsingEnglish.com © 2008 IELTS Speaking Part Two topic cards about Sports‚ hobbies and free time A-Z A Activity- see also “Favourite” and “Future” Describe an activity you like doing. You should say: - Where you do it - Who you do
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