assignmentutor™您的专属作业导师

assignmentutor-lab™ 为您的留学生涯保驾护航 在代写抽象代数abstract algebra方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写抽象代数abstract algebra代写方面经验极为丰富，各种代写抽象代数abstract algebra相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 数学代写|抽象代数作业代写abstract algebra代考|Permutations

Symmetric groups arise in a variety of natural contexts. In a 100-meter Olympic race, eight runners are given lane numbers. The function from the runner’s lane number to the rank they place in the race is a permutation of $S_8$. A cryptogram is a word game in which someone writes a message but replacing each letter of the alphabet with another letter and a second person attempts to recover the original message. The first person’s choice of how to scramble the letters of the alphabet is a permutation in $S_a$, where $a$ is the number of letters in the alphabet used. When someone shuffles a deck of 52 cards, the resulting reordering of the cards represents a permutation in $S_{52}$.
We need a few convenient ways to visualize and represent a permutation on ${1,2, \ldots, n}$.

Directed Graph. A visual method of representing a permutation $\sigma \in S_n$ involves using a directed graph. Each element of ${1,2, \ldots, n}$ is written as a point on the plane and we draw an arrow from $a$ to $b$ if $f(a)=b$. In this way, a permutation will create a directed graph in which one arrow leaves each point and arrives at each point. See Figure $1.7$ for an example.
Chart Notation. Another way of writing a permutation is to record in a chart or matrix the outputs like
$$\sigma=\left(\begin{array}{cccc} 1 & 2 & \cdots & n \ \sigma(1) & \sigma(2) & \cdots & \sigma(n) \end{array}\right) .$$
Using the chart notation, the permutation in Figure $1.7$ is written as
$$\sigma=\left(\begin{array}{llllllll} 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \ 3 & 8 & 7 & 4 & 6 & 2 & 1 & 5 \end{array}\right) .$$

## 数学代写|抽象代数作业代写abstract algebra代考|Inversions of a Permutation

Permutations play a central role in combinatorics, a field that studies techniques for counting the possible arrangements in any kind of discrete structure. We end this section with a brief discussion on the inversions of a permutation. This concept will come in handy when we discuss even and odd permutations in the next sections.

As a motivating example, suppose that we consider 5 events in history and attempt to remember the order in which they occurred. There are $5 !=120$ possible orderings of this time line. Suppose that we number the events in historical order as $E_1, E_2, E_3, E_4, E_5$ and suppose that someone guesses the historical order as $G_1, G_2, G_3, G_4, G_5$. Any guess about their historical order corresponds to a permutation $\sigma \in S_5$ via
$$G_{\sigma(i)}=E_i \quad \text { for all } i \in{1,2,3,4,5} .$$
This means that the person guessed the actual $i$ th historical event to be the $\sigma(i)$ th event in chronological order.

Suppose that someone guesses the chronological order of the births of five mathematicians and puts them in the following order.

The corresponding permutation is $\sigma=(132)(45)$.
What is a natural way to evaluate how incorrect the guess is? If a guess was correct except for interchanging the first two, i.e., $\sigma=(12)$, that should not be considered egregious. The worst guess would completely reverse the chronological order, i.e., $\sigma=(15)(24)$. A measure of incorrectness for the guessed ordering is to count the number of inversions.

# 抽象代数代写

## 数学代写|抽象代数作业代写abstract algebra代考|Permutations

$$\sigma=\left(\begin{array}{lllllll} 1 & 2 & \cdots & n \sigma(1) & \sigma(2) & \cdots & \sigma(n) \end{array}\right) .$$

$$\sigma=\left(\begin{array}{lllllllllllllll} 1 & 2 & 3 & 4 & 5 & 6 & 7 & 83 & 8 & 7 & 4 & 6 & 2 & 1 & 5 \end{array}\right) .$$

## 有限元方法代写

assignmentutor™作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

assignmentutor™您的专属作业导师
assignmentutor™您的专属作业导师