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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I. Food Manufacturing Industry in Philippines Food manufacturing‚ which includes food and beverage processing‚ remains the Philippines most dominant primary industry. The industry is worth a gross added value of more than $2 billion and grew by 3.2 percent. The Philippines Bureau of Food and Drugs Statistical Report of Establishments lists a total number of 11601 food processing establishments nationwide. Most of the companies are owned by a single proprietor that is common among micro‚ cottage
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Alexander Electronics Ltd. Alexander Electronics Ltd. (AEL) is a retailer of home electronics‚ software‚ music‚ and video games in a medium-sized Canadian city. The store has been in business for many years and has grown along with the community. Recently‚ AEL’s owner decided to sell the store because he felt he was too old for the rigours of operating it. Ryan Evans has expressed interest in buying AEL and he and the current owner have been negotiating for several months. Mr. Evans has worked
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Alex Rider: Stormbreaker 1) I liked this book. It was filled with action and suspense. But I didn’t like how it was far-fetched. A 14 year old that knew all different types of karate‚ languages‚ moves‚ and almost taught like a spy from birth. But other than that‚ I really liked the book. I like how everything was detailed. 2) A. The main characters are Alex Rider‚ Ian Rider (dead‚ but an important name)‚ Yassen Gregorovich‚ and Herold Sayle. B. The setting of this book is Present day in London
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“The way records were sold was completely ridiculous. The covers were brown‚ tan or green paper; they were not in the least bit attractive‚ and lacked any form of sales appeal” – these are the words of Alex Steinweiss‚ the creator of album artwork‚ way back in 1939. Before Steinweiss’ revolutionary creation‚ there was quite simply no such thing as an album cover; vinyl recordings were available to buy in the back of appliance stores‚ where one would enquire for the particular title of a recording
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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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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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Facilitate Continuous Improvement BSBMGT516C 1. Select an area for improvement in your workplace and create a Continuous Improvement Plan for that area. Include in your plan – using the templates provide: A. A brief outline of the issue you and/or your team have identified that needs improving and explain how it was identified‚ B. The that will need to be involved in the improvement process‚ C. How communication to the work team will occur‚ D. Coaching and Mentoring processes
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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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